Chapter 11, Problem 2PST

To determine

To find : The area of the shaded region.

Answer to Problem 2PST

Area of the shaded region is 114.9 ft².

Explanation of Solution

Given information :

  

The area of the shaded region = Area of rectangle ABCD - Area of semicircle .....(1)

  $\text{Area}\text{of}\text{rectangle}ABCD=lengthCD\times breadthBD$

  $=19\times 12$

  $=228f{t}^2$

  $\text{Area}\text{of}\text{semicircle}\text{=}\Pi {\text{r}}^2$

As r = Half of AC = 6ft

Implies,

  $\text{Area}\text{of}\text{semicircle}\text{=}\Pi {\text{r}}^2$

  $=\frac{22}{7}\times 6^2$

  $=113.14f{t}^2$ .

Therefore the area of shaded region = $228-114.14$ , using equation (1).

  $=114.86=114.9f{t}^2$ .

Thus the area of the shaded region is $114.9f{t}^2$ .