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This section will focus on how to calculate the Area of a Regular Polygon. We recall that a polygon is regular if all of its sides are congruent and if all of its interior angles are congruent. Remember that congruent means identical.
Finding the Area of a Regular Polygon. Work with a partner. Use dynamic geometry software to construct each regular polygon with side lengths of 4, as shown. Find the apothem and use it to fi nd the area of the polygon. Describe the steps that you used.
We can use Green’s Theorem to find a formula for the area of a polygon P in the plane with corners at the points (x , y ), (x , y ), . . . , (x , y ) (reading counterclockwise around P ). ).
Theorem: Area of a Regular Polygon. The area of a regular n-gon with side lengths (s) is half the product of the apothem (a) and the perimeter (P), so. = 1⁄2 aP, or A = 1⁄2 a • ns. The number of congruent triangles formed will be the same as the number of sides of the polygon.
4 Απρ 2015 · Complete a general formula in words: Area of a regular polygon - Example 2 How can you calculate the area of other regular polygons? height = base = 1.3 m Solution A. What is the area of this sandbox, which has the shape of a regular heptagon? Round your answer to one decimal place.
Chapter 11: Perimeter and Area 98 Perimeter and Area of a Triangle 100 More on the Area of a Triangle 101 Perimeter and Area of Quadrilaterals 102 Perimeter and Area of Regular Polygons 106 Circle Lengths and Areas 108 Area of Composite Figures Chapter 12: Surface Area and Volume 111 Polyhedra 112 A Hole in Euler’s Theorem 113 Platonic Solids ...
Objectives. 1 To find the area of a regular polygon. Examples. 1 Finding Angle Measures. 2 Finding the Area of a Regular Polygon. 3 Real-World Connection. Math Background. A regular n-gon can be constructed by using n adjacent congruent angles with measure 360. n .
