So, the area of polygon ABCDEFG is given by the sum of the area of trapezium ABCG and CDFG and the area of triangle DEF. The formula calculates the area of a pentagon, \ (A = \frac {5} {2} \times s \times a\) Where \ (s\) is the side of the pentagon and \ (a\) is the length of the apothem. area = n a cot (/n)/ 4. A = area The most popular, and usually the most useful formula is the one that uses the number of sides nnn and the side length aaa: However, given other parameters, you can also find out the area: The circumcircle is the circle that passes through all the polygon's vertex: you can learn how to calculate its center in the case of a triangle at our circumcenter of a triangle calculator. Ans: Area of \(ABCD = \;{\rm{Area\;of\;trapezium}}\;AECD\; + \;{\rm{Area\;of}}\;\Delta BCE\)\( = \frac{1}{2} \times \left( {{b_1} + {b_2}} \right) \times h + \frac{1}{2} \times b \times h\)\( = \frac{1}{2} \times (4 + 6) \times 5 + \frac{1}{2} \times 3 \times 6\;{{\rm{m}}^2}\)\( = 25 + 9\;{{\rm{m}}^2}\)\( = 34\;{{\rm{m}}^2}\), Q.5. The fields in which the specified geometry properties will be calculated. Add the different areas together to find the total area of the polygon. Its diagonal \(AD\) is drawn. We also learned to calculate the area of a polygon on a graph by finding the coordinates of the polygon. Then go back the other way, and multiply each y-coordinate by the x-coordinate below it. Regular polygons have a definite dimension to their sides, and thus their areas are easy to calculate compared to irregular polygons where the sides have no fixed dimension. So the area of this polygon-- there's kind of two parts of this. Learn more about Stack Overflow the company, and our products. The area of a polygon is the total space enclosed within the shape. Go to "Project >> Properties >> General" and change the units for distance and area measurements. The formula for the area of a regular polygonis. Note the differences between $area and area($geometry): Returns the area of the current feature. Calculating area of polygon considering relief in ArcGIS Desktop? The units are in place to give an indication of the order of the calculated results such as ft, ft2 or ft3. If you need to calculate the area of an irregularly-shaped polygon, keep reading to learn how! Select a datatype (i.e. So let's start with the area first. For finding the area of a polygon that is a little complex, or its formula is not defined, we split the figure into triangles, squares, trapezium, etc. If the polygon has five sides, it is called a pentagon. While the farmer has begun to learn more about SI units, he is as yet uncomfortable with their use and decides that his only viable option is to construct a pool in the form of an equilateral triangle with sides 77 ft in length, since any other variation would either be too large or small. Degrees Decimal Minutes ( DDD MM.mmm'). Q.4. These polygons each have their own region. Q.3: What is the easiest way to calculate the area of any regular polygon?Ans: The easiest way to calculate the area of a polygon is to divide it into triangles and apply the area of a triangle. \(A = \frac{1}{2} \times a \times P\), where, \(A\)is the polygon area, \(a\) is the apothem, and \(P\) is the perimeter. For more in-depth learning, check out Miacademy.co (https://www.parents.miacademy.co/), an online learning platform with lessons and practice games that go along with our videos. The World Geographic Reference System is based on the geographic system of latitude and longitude, but using a simpler and more flexible notation. Instead, there are just two multiplications, five additions, and possibly one division by two. Calculations are always If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. Calculating polygon areas in shapefile using QGIS, Geometry based automatic fill of fields in attribute table, How a top-ranked engineering school reimagined CS curriculum (Ep. Remember that the height needs to be perpendicular to the parallel sides. Finding the area of regular polygon when the SIDE and APOTHEM are known. Since the length and width are the same for a square, simply square the length of one of the sides to calculate the area. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. In a trapezoid, the parallel sides are referred to as the bases of the trapezoid, and the other two sides are called the legs. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 2023 Mathmonks.com. Using the field calculator is probably a better idea, though, as it doesn't require the creation of a new shapefile. The semi-major axis of an ellipse, as shown in the figure that is part of the calculator, is the longest radius of the ellipse, while the semi-minor axis is the shortest. A polygon is a closed plane figure bounded by straight line segments. This article has been viewed 1,460,463 times. A parallelogram is a special type of quadrilateral. Hence 1/45 (5+25) (10) 2 = 172.05 square cm. Now there is a new (temporary) Layer created. Enter any 1 variable plus the number of sides or the polygon name. In the example, we will calculate the area of a triangle using the coordinates. Calculating polygon area in QGIS without adding new field, Taking only the largest polygon from MultiPolygon layer in QGIS. Let\({b_1}\)and \({b_2}\)be the lengths of these bases. Having had an argument with her father about her excessive use of social media, she decides to prey on her father's fear of the unknown, and belief in the supernatural in order to prank him. More specifically: Formula above = integral_permieter (-y dx + x dy) = integral_area ( (- (-dy)/dy+dx/dx)dydyx = 2 Area - David Lehavi Jan 17, 2009 at 6:44 6 The link in the post is dead.Does anyone have another? It is calculated in the units set in the project settings. Unless otherwise noted, area and length properties are planar measurements using 2D Cartesian mathematics. There are six of these sides to the hexagon, so multiply 20 x 6 to get 120, the perimeter of the hexagon. First, number the vertices in order, going either clockwise or counter-clockwise, starting at any vertex. Learn more about length and area units in geoprocessing tools The geodesic length and area properties use a shape-preserving algorithm. If not getting very accurate area calculations does not bother you (or if you do not want to play with different options in the field calculator as mentioned by some of the answers and comments above), in the current version of QGIS (i.e., QGIS 3.12) there is an easy way to deal with this. Find the area of each triangle and then add the areas of two triangles which provides the quadrilateral area. The distance between the bases is called theheightof the Trapezium. First, we must calculate the perimeter using the side length. square. a = side length You use the following formula to find the area of a regular polygon: So what's the area of the hexagon shown above? Through all of her metaphorical musings and tribulations involving space, it almost becomes believable that the farmer's daughter somehow influenced the massive octahedral diamond asteroid falling squarely, but safely upon their farmland, which she interprets as representing her journey, formation, and eventual homecoming. Find the area of each smaller shape, then add the areas together to find the area of the whole shape. We can find the area of a polygon on a graph as well. Assuming it's not a square or rectangle, you would have to subdivide the figure into smaller sections consisting of squares, rectangles, triangles, and other shapes whose areas can be easily calculated. If total energies differ across different software, how do I decide which software to use? Then going up the other side of the polygon subtracts all the yellow area shown here, because when a side is going up, Y0-Y1 is a negative number. Regular Polygon. So, the area is \(5\,{\rm{cm}} \times 5\,{\rm{cm}} = 25\,{\rm{c}}{{\rm{m}}^2}\). equilateral triangle and when n = 4 is is a Check out 23 similar 2d geometry calculators , Using the area of regular polygon calculator: an example. The length unit will be international feet. and semi-minor axes, The Farmer and his Daughter Falling out of Orbit. Calculate the area of a regular pentagon with side 12 cm and apothem of 7.5 cm. But the trick is to add when they go forwards (positive width), and subtract when they go backwards (negative width). + (xny1 ynx1)/2 |. Where x n is the x coordinate of vertex n, y n is the y coordinate of the nth . For instance, to calculate the area of a triangle, use the formula x base x height. If 103 represents "x3," then you can see that x = 10. The tool should be self explanatory and will allow you to calculate area in units of your choice regardless of projection. Cite this content, page or calculator as: Furey, Edward "Regular Polygon Calculator" at https://www.calculatorsoup.com/calculators/geometry-plane/polygon.php from CalculatorSoup, Let \(h\) be the height. We can finally calculate the area of the regular inscribed polygon. Height of trapezium ABCG = 3 cm Height of trapezium CDFG = (6 - 3) = 3 cm Height of triangle DEF = (8 - 6) = 2 cm Area of trapezium ABCG = (sum of parallel sides) height/2 = (4 + 7)3/2 = 33/2 = 16.5 cm 2 Area of \(\Delta ABC\; = \;\frac{1}{{2\;}} \times {\rm{base}} \times {\rm{height}} = \;\frac{1}{{2\;}} \times BC \times AM.\). By signing up you are agreeing to receive emails according to our privacy policy. If you list the points in a clockwise order instead of counterclockwise, you will get the negative of the area. Weisstein, Eric W. "Regular Polygon." The straight-line segments that make up a polygon are called the sides of a polygon, and the endpoints of the line segments are called vertices of the polygon. Why area of intersection differs from total area of polygon? Learn more about length and area units in geoprocessing tools. A = 1 2 l 4 R 2 l 2 2 = l 4 R 2 l 2 4. Adds information to a feature's attribute fields representing the spatial or geometric characteristics and location of each feature, such as length or area and x-, y-, z-coordinates, and m-values. Being a doting father, the farmer acquiesces to his daughter's request and proceeds to plan the construction of his triangular pool. Where n - number of sides, a - side length. There are two new domains for you to unlock including the " Somalata Inland . The following video gives formulas and examples to find the area of squares, rectangles, triangles, parallelograms . Parabolic, suborbital and ballistic trajectories all follow elliptic paths. Try using the "Identify Features" tool (Ctrl+Shift+I) from the Attributes Toolbar. What is the difference between regular and irregular polygon?Ans: Regularshapes have sides that are all equal and interior angles that are all equal. This formula for area is a very efficient computation as it doesn't involve roots or trigonometric functions. This is more reliable measurement of area than Area () because it takes into account the Earth's curvature. Example: Find the area of the regular polygon with three sides and with a 6 cm base and 10cm height l. The triangle formula for finding area will be applied here since it is a 3gon : 1/2 base height. We calculate the area for each part and then add them up to obtain the polygon area. Simple deform modifier is deforming my object. If you want to find the area of a regular polygon, simply use the formulas described above. The coordinate format will be Decimal Degrees. The features with a field that will be updated with geometry calculations. At long last, fortunately for the farmer's daughter and her family, hope does appear, but not in the form of a Prince Charming, but rather as a sign from the supposed heavens. n = number of sides All units will be calculated in the units of the projection, so you probably want to project it to a projection that uses feet or meters before doing that, rather than lat/lon. Select your input layer, give the field a proper name (area for example). See Tools that modify or update the input data for more information and strategies to avoid undesired data changes. Not knowing where to start, she walks around town talking to a variety of strangers all of whom seemingly have endless founts of wisdom and advice, where she learns about crop circles and their association with aliens and unidentified flying objects as well as many other topics that ignore all scientific and logical explanations. Is there a generic term for these trajectories? About area($geometry) from the QGIS Documentation: Returns the area of a geometry polygon object. As an example, let's use a hexagon (6 sides) with a side ( s) length of 10. Specifies the coordinate format in which the x- and y-coordinates will be calculated. The coordinate format will be World Geographic Reference System. Thanks to all authors for creating a page that has been read 1,460,463 times. The following Python window script demonstrates how to use the CalculateGeometryAttributes function. The standard unit of area in the International System of Units (SI) is the square meter, or m2. As we know, a polygon can be regular or irregular. Unfortunately for the farmer, he does not consider the fact that the maintenance costs of a pool for one year alone could likely pay for his children to visit any pool or water theme park for years to come. If you want to calculate the regular polygon parameters directly from equations, all you need to know is the polygon shape and its side length: Area. }}\) Find the area of the polygon \(ABCD\). The farmer's daughter proceeds to measure the area of one of the rhomboidal faces of her newly found symbol of life: Unfortunately for the farmer's daughter, the appearance of the enormous diamond drew attention from all over the world, and after sufficient pressure, she succumbs to the human within her, and sells the diamond, the very representation of her life and soul, to a wealthy collector, and proceeds to live the rest of her life in lavish indulgence, abandoning her convictions, and losing herself within the black hole of society. You can select an existing field or provide a new field name. A parallelogram is a simple quadrilateral which has two pairs of parallel sides, where the opposite sides and angles of the quadrilateral have equal lengths and angles. won't this save your values as strings? The area unit will be square US survey yards. If each polygon angle is less than \({180^ \circ }\), the polygon is called a convex polygon, and if at least one angle of a polygon is more than \({180^ \circ }\), it is called a concave polygon. As a small thank you, wed like to offer you a $30 gift card (valid at GoNift.com). Like we split a quadrilateral into triangles to find its area, we can also split any polygon into triangles, trapeziums, etc., to find its area. To calculate the area, use the formula for the area of a regular hexagon: This particular hexagon is equal in size to any one of the 18 elements in the primary mirror of the James Webb Space Telescope. Divide the result by 2 to get the area. Were committed to providing the world with free how-to resources, and even $1 helps us in our mission. The coordinate format will be United States National Grid. What is this brick with a round back and a stud on the side used for? Degrees Minutes Seconds (<+|-> DDD.MMSSSss). From The equation for calculating the area of a circle is as follows: The Farmer and his Daughter Circle of Li(f)es. Click Run. If you want to calculate the area of a regular polygon using parameters other than the side length, check out this regular polygon calculator. Lets look at some instances of how to get the area of a regular polygon. Octagon area formula: A = 2 (1 + 2) a Annulus area formula: A = (R - r) Quadrilateral area formula: A = e f sin (angle) Regular polygon area formula: A = n a cot (/n) / 4 Want to change the area unit? Genshin Impact patch 3.6 added the Girdle of the Sands, a new area in Sumeru's desert. It is a figure bounded or enclosed by three-line segments. https://www.calculatorsoup.com - Online Calculators. MathWorld--A Wolfram Web Resource. The coordinate system of the input features is used by default. An ellipse is the generalized form of a circle, and is a curve in a plane where the sum of the distances from any point on the curve to each of its two focal points is constant, as shown in the figure below, where P is any point on the ellipse, and F1 and F2 are the two foci. Calculate the area of a regular pentagon with side 12 cm and apothem of 7.5 cm. Does the 500-table limit still apply to the latest version of Cassandra? With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. area). At this point in time, through extreme effort and perseverance, the farmer has finally sold his 21,780 sq ft plot of land and has decided to use some of the money earned to build a pool for his family. Hence this can be used as a tool to identify the cyclic path or sequence of a given set of points forming a polygon. Note that just because a projection has meters as its map unit, doesn't mean it represents areas accurately. Pro tip: Double-jumping into a wall run will give you more height at the start, thus . Let us learn the basic approach for determining the area of both types, separately. Programmatically finding polygons which are >90% overlapped by another vector polygon layer using QGIS? Area of an Irregular Polygon. A regular polygon is a polygon that is both equiangular and equilateral. There is an operator $area that will calculate the area of each row in the table. Another six years have passed, and his daughter has grown into a strong, beautiful, powerful, confident 15-year-old ingrate solely focused on seeking external validation from acquaintances and strangers on social media while wholeheartedly ignoring genuine support from immediate family and friends. Where \(s\) is the side of the pentagon and \(a\) is the length of the apothem. Use coupon code VIDEOSPECIAL for a discount. The best answers are voted up and rise to the top, Not the answer you're looking for? Irregularshapes have sides and angles of any length and size. The area of any regular polygon is given by the formula: Area = (a x p)/2, where a is the length of the apothem and p is the perimeter of the polygon. An irregular polygon is a polygon with interior angles of different measures. The area of the trapezoid is calculated as follows: A circle is a simple closed shape formed by the set of all points in a plane that are a given distance from a given center point. To see how this equation is derived, see Derivation of regular polygon area formula. On the site, kids can interact safely in a moderated environment and share their artwork, videos, and ideas with each other. As the farmer has now become more comfortable with SI, he is able to be more creative with his use of units, and can build a more reasonably sized ramp while adhering to his daughter's demands. Next, select the polygon file that you want to calculate area on and right click. The calculator computes the total area and also outputs all triangles it is used for calculation. The foot was defined to be exactly 0.3048 meters in 1959 after having changed over an extensive period of time, as historically, the human body was often used to provide a basis for units of length, and unsurprisingly, was inconsistent based on time and location. To determine the surface area of regular polygons with n sides (where each side is represented as s), we use the formula given below: Find the area of a regular polygon with perimeter of 44 cm and apothem length of 10 cm. The coordinate format will be Degrees Minutes Seconds packed into a single value with positive or negative direction component at the beginning (<+|-> DDD.MMSSSss). Select the polygon layer to calculate area. Some types of polygons have their own special formulas that you can use to find the area. The coordinate system in which the coordinates, length, and area will be calculated. At times with the help of apothem, we can find the area of a polygon. Unfortunately for the farmer, he lives in an area predominated by foreign investors with smaller feet, who felt that they should be getting more square feet for their money, and his land remains unsold today. There are 7 references cited in this article, which can be found at the bottom of the page. y = exterior angle The area is widthheight: 1.94 3.495 = 6.7803 Add Them All Up Now add them all up! Using this information: The farmer's plot of land, which has an area of 21,780 square feet, equates to half an acre, where an acre is defined as the area of 1 chain by 1 furlong, which is defined by something else, and so on, and is why SI now exists. It is easier to find the area for polygons because their dimensions are set and known. Rectangles, rhombuses, and squares are all special cases of parallelograms. Scroll down to Expression and either click Geometry -> $area or type in $area into the left box. GEOREF (World Geographic Reference System). You can view it as the height of the equilateral triangle formed by taking one side and two . I wrote a script specifically for this. The five angles present in the regular pentagon are equal. Always double-jump into wall runs. In the example, we will calculate the area of a triangle using the coordinates. When the number of sides, n, is equal to 3 it is an If x and y are vectors of the same length, then polyarea returns the scalar area of the polygon defined by x and y. Calculates side length, inradius (apothem), circumradius, area and perimeter. Good for homeschoolers, Parents, Teachers, or anyone with kids in grades K-8.Miacademy also offers many hands-on learning activities including a business simulation, writing in the Miacademy weekly, and creating artwork. -> Number Since version 1.7 Function bundle: Geometry Returns the geodetic area of the input geometry or Feature in the given units. r = inradius (apothem) If a polygon is regularthat is, all of its sides are the same lengthyou can easily find the area given the side length and the apothem. When a gnoll vampire assumes its hyena form, do its HP change? All units will be calculated in the units of the projection, so you probably want to project it to a projection that uses feet or meters before doing that, rather than lat/lon. To learn the steps follow the link given below: Your email address will not be published. In current versions of QGIS if your data is in a Geographic CRS you can use the function transform() to project the geometries to a projected system (Preferably an equal area one) without the need to duplicate your data. 4. You know that the side across from the 60 degree angle has length = x3, the side across from the 30 degree angle has length = x, and the side across from the 90 degree angle has length = 2x. The shoelace formula, also known as the shoelace algorithm, Gauss's area formula, and the surveyor's formula, is all that's required to calculate the area of a polygon. Only regular polygons have apothems. The coordinate format will be Degrees Decimal Minutes with positive or negative direction component at the beginning (<+|-> DDD MM.mmm'). Level up your tech skills and stay ahead of the curve. Triangles, squares, rectangles, pentagons, hexagons, and other polygons are utilised in geometry. Extracting arguments from a list of function calls. All sides are equal length placed around a common center so that all angles between sides are also equal. Now, as we understand what a polygon is, let us have a quick look at what an area is. Note the differences between $area and area ($geometry): Q.4. If we are looking to find the area of other basic polygons such as triangle, rectangle, parallelogram, rhombus, trapezoid, kite, pentagon, and hexagon, we can also use their standard formulas that are given below: For determining the area of a polygon given on a coordinate plane, we will use the following formula: Area (A) = | (x1y2 y1x2) + (x2y3 y2x3). The coordinate format will be Degrees Minutes Seconds with cardinal direction component at the end (DDD MM' SSS.ss" ). We have n triangles with equal area, so the total area will be n multiplied by the area of a single triangle. Step 1: Enter the number of sides and side length in the input field (Example: n=5, S= 3) Step 2: Now click the button "Solve" to get the regular polygon area Step 3: Finally, the area of the regular polygon will be displayed in the output field (I.e., Area of Regular Polygon, A= 15.485 square units) What is Meant by the Area of Regular Polygon? Find the area of a regular polygon with perimeter of 44 cm and apothem length of 10 cm. \( = \frac{1}{2} \times 8 \times 3 = 12\) square units. Before starting, make sure that the Hide Derived Attributes from Results option is unchecked. If you know the apothem and the side length, simply use the formula area = x perimeter x apothem. The area of a kite is half the product of the lengths of its diagonals. Multiply the x-coordinate of each vertex by the y-coordinate of the vertex below it in the table and add all the products together. The area of a polygon is the region of space occupied in a \(2 D\) plane, irrespective of its shape, like a triangle, square, parallelogram, or trapezium. That is super important. Let us look at the figure below and understand the parameters required to make a polygon. Include your email address to get a message when this question is answered. Several coordinate formats, including Degrees Minutes Seconds, Degrees Decimal Minutes, and others, require the calculation to be performed in a text field. Your email address will not be published. Honkai: Star Rail is Hoyoverse's leap into turn-based combat in a mobile (and PC) game that brings out new versions of familiar characters, beautiful art, and an . Any other base unit can be substituted. The formula is as follows: The Farmer and his Daughter - Triangle Daze. If the polygon has six sides, it is called a hexagon and so on. NCERT Solutions for Class 12 Chemistry Chapter 15 Polymers, 9th CBSE Board Study Material: Access Here for Free, NCERT Solutions for Class 12 Biology Chapter 10 Microbes in Human Welfare, NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations, NCERT Solutions for Class 12 Maths Chapter 11 3D Geometry, NCERT Solutions for Class 12 Chemistry Chapter 1 The Solid State, NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions, NCERT Solutions for Class 12 Maths Chapter 13 Probability. The above area of polygon formula is used when the length of any side and the corresponding height isknown or given. There will be two attributes: "Area (Cartesian)" and "Area (Ellipsoidal - EPSG:7019)". (See also: Computer algorithm for finding the area of any polygon .) To calculate the area of a regular polygon given the radius, apply the formula: area = n a cot (/n) / 4 where: n - Number of sides of the polygon; a - Length of the side; and cot - Cotangent function ( cot (x) = 1/tan (x) ). Leading AI Powered Learning Solution Provider, Fixing Students Behaviour With Data Analytics, Leveraging Intelligence To Deliver Results, Exciting AI Platform, Personalizing Education, Disruptor Award For Maximum Business Impact, Copyright 2023, Embibe. This area of a regular polygon calculator can help as you can guess in determining the area of a regular polygon. The coordinates of the vertices of the triangle are \(A( 1,2),B( 3, 1)\) and \(C(5, 1)\). To find the area of any polygon with the side length and the apothem we must know the equation for the area of a polygon which is. Even more unfortunately for the farmer, his 7-year-old daughter who has recently traveled to Egypt vicariously through Dora the Explorer, has fallen in love with triangles, and insists that the pool not only be triangular in shape, but also that the measurements must only include the number 7, to represent her age and immortalize this point of her life in the form of a triangular pool. Be really careful with this. This article was co-authored by David Jia. Two years have passed since the farmer's pool was completed, and his daughter has grown and matured. Simply click on the unit name, and a drop-down list will appear. To find the area of an irregular polygon you must first separate the shape into regular polygons, or plane shapes. (Trick: Divide the polygon into two rectangles), To solve the given problem, let us divide the given figure into two rectangles ABFE and GFDC.Now, as we know,Area of a rectangle = l x b, here l = length and b = breadthIn rectangle ABFE, lengths (AB = FE) = 18 cm and breadths (AE = BF) = 16 cmThus, area of rectangle ABFE = (18 x 16) = 288 cm2Similarly, in rectangle GFDC, lengths (GF = DC) = 14 cm and breadths (GD = FC) = 8 cmThus, area of rectangle GDFC = (14 x 8) = 112 cm2Since, area of polygon ABCDE = area of rectangle ABFE + area of rectangle GDFC= (288 + 112) cm2= 400 cm2. Apothem area formula. Provided below are equations for some of the most common simple shapes, and examples of how the area of each is calculated. Area of Polygon. The area unit will be square US survey nautical miles. To compute the area of a pentagon with side 3, you can directly apply the formula: If you know the apothem of a regular polygon, you can compute the area with the formula: 1.509 m. If you want to know how to find the area of a variety of polygons, just follow these steps. Use it to try out great new products and services nationwide without paying full pricewine, food delivery, clothing and more. What positional accuracy (ie, arc seconds) is necessary to view Saturn, Uranus, beyond?
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calculate area of a polygon