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Calculating the area of a polygon can be as simple as finding the area of a regular triangle or as complicated as finding the area of an irregular eleven-sided shape. If you want to know how to find the area of a variety of polygons, just follow these steps.
This article was co-authored by David Jia. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. 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. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 1,414,778 times.
Co-authors: 51 Updated: August 29, 2022 Views: 1,414,778 Article Rating: 53% - 8 votes Categories: Calculating Volume and Area Article SummaryX A polygon is any kind of closed, 2-dimensional shape with at least 3 straight sides and no curves. If a polygon is regular—that is, all of its sides are the same length—you can easily find the area given the side length and the apothem. The apothem is the distance from the exact center of the polygon to the center of any of the sides. If you know the apothem and the side length, simply use the formula area = ½ x perimeter x apothem. You can find the perimeter by adding together the lengths of all the sides, or multiplying the length of a side by the number of sides. For example, say you have a hexagon with an apothem that has a length of 3 units, and each side has a length of 7 units. Multiply 7 by 6 (the number of sides in the hexagon) to find the perimeter of 42 units. Multiply 42 x 3 x ½ to get an area of 63 square units. Some types of polygons have their own special formulas that you can use to find the area. For instance, to calculate the area of a triangle, use the formula ½ x base x height. For a rectangle, all you need to do is multiply length times width. Since the length and width are the same for a square, simply square the length of one of the sides to calculate the area. If your shape is a trapezoid, add together the lengths of the two parallel sides, then multiply the sum by the height of the trapezoid. Divide the result by 2 to get the area. In other words, use the formula area = (base1 + base2) x h x ½. When you’re dealing with an irregular polygon, things get a little trickier. The easiest way to find the area of an irregular polygon is to plot it on a graph and find the coordinates of each of the vertices, or corners. Create a table with the x-coordinate of each vertex in one column, and the y-coordinate of each vertex in the next column. 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. Then go back the other way, and multiply each y-coordinate by the x-coordinate below it. Add together those products as well. Subtract the sum of the second set of products from the sum of the first set, then divide the difference by 2 to find the area of the polygon. If you need to calculate the area of an irregularly-shaped polygon, keep reading to learn how!
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