Question: How do we find the area of regular polygons?

Answer: Well you can divide a regular polygon into congruent isosceles triangles by drawing segments to each vertex, as shown in the following figure:

Regular Polygon Area Conjecture
The area of a regular polygon is given by the formulas: A=nas and A=Pa
                                                             2              2
Where A is the area, P is the Perimeter, a is the apothem, s is the length of sides, and n is the number of sides.
The apothem is the perpendicular bisector from the center of the polygon to the side.

As seen in the image above, to find the area all you have to do is follow either one of the formulas, right now i am going to use the formula: A=nas
                                                   2
So i will have to multiply 7(n) times 7(a) times 10(s) and divide it by 2. Thus, the area of the heptagon will be 245 square cm.


NOW YOU TRY! :D


Find the area of the following polygon: