Chapter 11.4, Problem 14PPS

  

To determine

To find: The area of the floor to be carpeted.

Answer to Problem 14PPS

The area of the floor to be carpeted is $363{\text{ft}}^2$ .

Explanation of Solution

Given:

The given figure is:

  

Calculation:

To find the area of the figure, add the area of the trapezium and area of rectangle.

Area of trapezium is calculated as:

  $\begin{array}{c}\text{Area of trapezium=}\frac{1}{2}\left(\text{sum of the length of parallel sides}\right)\text{×}\left(\text{distance between the parallel sides}\right)\\ =\frac{1}{2}\left(9+24\right)\cdot \left(6\right)\\ =99\end{array}$

The area of shaded region is calculated as:

  $\begin{array}{c}\text{Area of figure}=\text{Area of rectangle}+\text{Area of trapezium}\\ =\text{length×breadth}+99\\ =11\text{×}24+99\\ =363\end{array}$

Therefore the area of the floor to be carpeted is $363{\text{ft}}^2$ .