Chapter 11.4, Problem 37HP

To determine

To find: The diagram for the composite figure that have same area such that the composite area have rectangle and a trapezoid and make the other composite figure out of triangle and the rectangle.

Answer to Problem 37HP

The required figure are shown in Figure 1 and 2.

Explanation of Solution

Calculation:

Consider the two composite figure of the same area is $10{\text{cm}}^2$ and the first composite figure consists of the rectangle and the trapezoid.

Consider the rectangle has $b=4\text{cm}$ and $h=1\text{cm}$ .

Then, the trapezoid is with $b_1=2\text{cm}$ , $b_2=4\text{cm}$ and $h=2\text{cm}$ .

Thus, the composite area of the figure is,

  $\begin{array}{c}A=bh+\left(\frac{b_1+b_2}{2}\right)h\\ =4+\left(\frac{4+2}{2}\right)2\\ =4+6\\ =10\end{array}$

The first composite figure is shown in Figure 1

  

Figure 1

Consider the composite figure shown below in Figure 2

  

Figure 2

Then, the area of the above figure is,

  $\begin{array}{c}A=bh+\frac{1}{2}bh\\ =4\left(2\right)+\frac{1}{2}\left(4\right)\left(1\right)\\ =8+2\\ =10\end{array}$