Exercise 44 Page 42

Let's divide the regular polygon into 8 congruent triangles, where each has a base b and a height h.

The area of the octagon is equal to the sum of the areas of the 8 identical triangles. We can calculate the area A_T of each of them using the formula for the area of a triangle. In the formula b stands for the base and h stands for the corresponding height of the triangle. A_T=1/2bh If we multiply the above expression by 8, we get the the total area of the 8 triangles making up the polygon. Therefore, we get the formula for the area A of the regular polygon. A=8 A_T ⇔ A=8( 1/2bh) Let's simplify the expression.

A=8(1/2bh)

RemovePar

Remove parentheses

A=8* 1/2bh

MoveLeftFacToNumOne

a* 1/b= a/b

A=8/2bh

CalcQuot

Calculate quotient

A=4bh

We want to solve this formula for the height h, which means we need to isolate it on one side.

A=4bh

DivEqn

.LHS /4b.=.RHS /4b.

A/4b=h

RearrangeEqn

Rearrange equation

h=A/4b