Question

Find the area of the shaded region if the radius is 12 inches.

Answer 1

The area of a circle with radius r is given by the formula:

`A=\pi r^2`

The circular sector is 1/4 of the whole circle. Then the area is given by 1/4 of the area of a circle:

`A=(1)/(4)\pi r^2`

Substitute r=12 in and use 22/7 as the value for π:

`\begin{gathered} A=(1)/(4)*(22)/(7)(12in)^2 \\ =(1)/(4)*(22)/(7)*144in^2 \\ =(3168)/(28) \\ =(792)/(7) \\ =113.1428571\ldots \end{gathered}`

Then, the area of the shaded sector up to one decimal place is:

`113.1`