Chapter 11.6, Problem 33PPS

To determine

To calculate: The area of the given trapezoid.

Answer to Problem 33PPS

The area of trapezoid = 23.6 $y{d}^2$ .

Explanation of Solution

Given information: In the given trapezoid, two parallel bases given a = 24 ft and

b=14 ft, height(h) = $11\frac{1}{5}=\frac{11\times 5+1}{5}=\frac{55+1}{5}=\frac{56}{5}$ ft.

Formula used: Area of trapezoid = $\frac{1}{2}(a+b)\times h$

Calculation:

Area of trapezoid is

  $\begin{array}{l}\frac{1}{2}(a+b)\times h\\ =\frac{1}{2}(24+14)\times \frac{56}{5}\\ =\frac{1}{2}\times 38\times \frac{56}{5}\\ =\frac{2128}{10}\\ =212.8\end{array}$

So, the area of trapezoid = 212.8 $f{t}^2$

We know that, 1 $y{d}^2$ =9 $f{t}^2$

1 $f{t}^2$ = $\frac{1}{9}$ $y{d}^2$

212.8 $f{t}^2$ = 23.6 $y{d}^2$ [ To the nearest tenth]

$\therefore$ The area of the trapezoid = 23.6 $y{d}^2$