Chapter 1.5, Problem 44E

To determine

To write the formula for the area of the regular polygon in terms of $h$ and solve the formula for $h$ .

Answer to Problem 44E

The area of the polygon (Octagon) is $4bh$ and solving for $h$ , $h=\frac{A}{4b}$

Explanation of Solution

Given information :

Given polygon

  

The area of the polygon (Octagon) is contains $8$ triangles.

Thus, area is equal to $8$ times area of the triangle.

  $\begin{array}{l}\text{Area}\text{triangle}=\frac{1}{2}\times base\times height\\ =\frac{1}{2}\times b\times h\end{array}$

Hence, the area of the polygon (Octagon) is $A=\frac{8}{2}\times b\times h=4bh$

Solving for $h$ , $h=\frac{A}{4b}$