Area of Regular PolygonsNotice that every regular polygon can be divided into congruent triangles.

The number of triangles a polygon can be divided into depends on the number of sides of the polygon (ex. A hexagon can be divided into six congruent triangles, an octagon can be divided into 8 congruent triangles).

21

34

6

5

12

3

4

7

56

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Area of Regular PolygonsIf we know that each of the six triangles in the hexagon are congruent, how can

we find the area of the hexagon?

If we find the area of one of the triangles can we find the area of the hexagon?

Remember the area of a triangle is A = 1/2bh. Find the area of the hexagon below.

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4

Area of 1 Triangle _________

Area of Hexagon __________

Area of Regular PolygonsDoes the same technique work for the

octagon?

Find the area of the octagon below.

Area of 1 Triangle _________

Area of Octagon __________

12

8

Area of Regular PolygonsWhen finding the area of the hexagon and the octagon we used

the formula: A = 1/2bh(# of triangles)

The standard formula for Area of a Polygon is A = 1/2asn where

a is the apothem (the distance from the center of the polygon to the midpoint of one of the sides; aka - height of one of the triangles).s is the length of one side of the polygon (aka - base of one of the triangles).n is the # of sides of the polygon (aka - # of triangles).

Find the area of the octagon using the formula: A = 1/2asn

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Area of Regular PolygonsRemember the formula A = 1/2asn

What measurement do we get when we mulitply s (length of each side) and n (number of sides)? Doesn't it give us the distance around the polygon? What do we call that distance?

So, the area of a regular polygon can be written as A = 1/2asn or A = 1/2a___.

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The perimeter of the pentagon is 45 cm. Find the Area.

Area of Regular PolygonsLet's try one more!

Find the area of the shaded region if the apothem is 3 and AB is 12.

Remember, Area of a regular polygon is A = ___________

A B

C

DE

F