Chapter 11.5, Problem 33WE

(a)

To determine

To Complete: As the number of sides increases, the value of $a$ gets nearer to .....and the perimeter of polygon gets nearer to $2\pi r$ .

Answer to Problem 33WE

Radius

Explanation of Solution

Given: A regular polygon with apothem $a$ and radius $r$ is inscribed in a circle.

As the number of sides increases, the value of $a$ gets nearer to radius and the perimeter of polygon gets nearer to $2\pi r$ .

(b)

To determine

To Find: What formula do you get?

Answer to Problem 33WE

  $A=\pi r^2$

Explanation of Solution

Given: In the formula $A=\frac{1}{2}ap$ , replace $abyrandpby2\pi r$ .

  $A=\frac{1}{2}ap$

Replacing $a=randp=2\pi r$

  $\begin{array}{l}A=\frac{1}{2}r(2\pi r)\\ A=\pi r^2\end{array}$

We get the formula of area of circle.