Any regular n-gon can be changed to n isosceles congruent triangles by drawing all radii to the vertices of the polygon.
the area of a triangle = (1/2)(base)(height)
the area of one of these = (1/2)(side)(apothem)
where the apothem is the distance from the centre of the polygon to the side.
area of n-sided polygon
= (n/2)(side of polygon)(apothem)
If you are given the radius and the length of a side, you have to find the apothem first by Pythagoras
e.g. A 10sides polygon has a radius of 20 and a side of 8
let the height (apothem) be h
h^2 + 4^2 = 20^2
h^2 = 400-16
h = √384 = 8√6
area of 10-sides polygon
= (10/2)(8)(8√6)
= 320√6
Please help! I'm really confused on what it is asking.
Use the formula for area of a triangle to derive the formula for the area of a regular polygon.
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