How to Calculate the Area of a Polygon
The area of a polygon is a useful calculation in many areas of mathematics, science, engineering and construction. Depending on the situation, there are specific formulas for calculating the areas of specific polygons, and there are general formulas that work for all geometric shapes.
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Instructions
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Use the triangulation method to compute the area of irregular polygons. In this technique, you divide the geometric figure into triangles, calculate the area of each individual triangle and then add up the smaller areas to find the area of the entire figure. In general, if a polygon has n sides, you can divide it into (n - 2) triangles.
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Calculate the area of each triangle using the base/height formula:
Area = (1/2)bh
Alternatively, use Heron's formula:
Area = (1/4)sqrt[s(s - 2a)(s - 2b)(s - 2c)]
where a, b and c are the lengths of the sides of the triangle, and s = a + b + c.
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Use the tangent formula to compute the area of any regular polygon with n sides. A regular polygon is a geometric shape in which every side has the same length, and every corner has the same angle. The tangent formula is:
Area = [S^2 * n]/[4 * tan(180/n)]
where S is the length of each side, n is the number of sides and tan is the abbreviation for tangent, a trigonometry function. For example, use the tangent formula to compute the area of a regular hexagon -- six-sided figure -- where every side has length 10:
Area = [10^2 * 6]/[4 * tan(30)]
= [600]/[4(0.57735)]
= 259.81
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References
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