1. Area of Regular Polygons
Notice 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). 2 1 3 4 6 5 1 2 3 4 7 5 6 8

2. Area of Regular Polygons
If 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.
Area of 1 Triangle _________
Area of Hexagon __________ 6 4

3. Area of Regular Polygons
Does the same technique work for the octagon?
Find the area of the octagon below.
Area of 1 Triangle _________
Area of Octagon __________ 12 8

4. Area of Regular Polygons
When 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). 5 8
Find the area of the octagon using the formula: A = 1/2asn

5. Area of Regular Polygons
Remember 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___. 6
The perimeter of the pentagon is 45 cm. Find the Area.

6. Area of Regular Polygons
Let'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 D E F