Chapter 11.2, Problem 4CYU

To determine

To find: The amount of fabric needed to design at the right.

Answer to Problem 4CYU

The amount of fabric needed is $8.75{\text{ft}}^2$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

The given shape is the shape of the trapezoid with $h=\frac{5}{2}\text{ft}$ , $b_2=\frac{3}{2}\text{ft}$ and value of

$\begin{array}{c}{b}_1=\frac{1}{4}+\frac{3}{2}+\frac{1}{4}\\ =2\text{ft}\end{array}$

Then, the area of the trapezoid is obtained as,

  $\begin{array}{c}A=\frac{1}{2}\left(b_1+b_2\right)h\\ =\frac{1}{2}\left(2+\frac{3}{2}\right)\frac{5}{2}\\ =\frac{35}{8}\\ =4.375{\text{m}}^2\end{array}$

Then, the amount of fabric needed is,

  $2\left(4.375{\text{m}}^2\right)=8.75{\text{ft}}^2$