Chapter 8.2, Problem 42PPS

To determine

To find: The area of the face of the piece of the dog house.

Answer to Problem 42PPS

  $318{\text{ in}}^2$

Explanation of Solution

Given:

The upper face of the dog house is a trapezoid and its height is 12 inches.

  

Calculation:

The area of a trapezoid is given by

  $A=\frac{1}{2}\left(a+b\right)h$

Substituting $a=3h+1,b=h+4$

  $A=\frac{1}{2}\left(3h+1+h+4\right)h$

On simplifying

  $A=\frac{1}{2}\left(4h+5\right)h$

Substituting the value of h

  $\begin{array}{c}A=\frac{1}{2}\left(4\cdot 12+5\right)\cdot 12\\ =\frac{1}{2}\cdot 53\cdot 12\\ =318{\text{ in}}^2\end{array}$