Chapter 9.2, Problem 45E

To determine

To find: Whether the statement is correct or not.

Answer to Problem 45E

The statement is correct as the area of the sector is $\frac{s^2}{2}$ .

Explanation of Solution

Given:

The give statement is that “when the arc length of a sector equals the radius then the area 2 is given by $A=\frac{s^2}{2}$ ”.

Calculation:

Consider the formula to determine the arc length is,

  $s=r\theta$

Then, substitute $s=r$ and $\theta =1$ .

  $r=r\theta$

Then, the area of the sector is obtained as,

  $\begin{array}{c}s=\frac{1}{2}{s}^2\left(1\right)\\ =\frac{s^2}{2}\end{array}$