Chapter 11.2, Problem 25PPS

(a)

To determine

To find: The amount of fabric of each colour that is needed to buy.

Answer to Problem 25PPS

The area of red, orange, blue, green and blue colour each isyy13

  $24{\text{in}}^2$ and the area of purple fabric needed is $20{\text{in}}^2$ .

Explanation of Solution

Given:

The rhombus are congruent.

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

The length of the diagonals is calculated as,

  $\begin{array}{c}{d}_1=2\left(4\right)\\ =8\text{in}\end{array}$ and $\begin{array}{c}{d}_2=2\left(3\right)\\ =6\text{in}\end{array}$

Consider the area of the kite is of the form,

  $A=\frac{1}{2}{d}_1{d}_2$

Then, the area of the fabric needed of red, orange, blue, green and blue colour each is obtained as,

  $\begin{array}{c}A=\frac{1}{2}\left(8\right)\left(6\right)\\ =\frac{1}{2}\left(48\right)\\ =24{\text{in}}^2\end{array}$

The area of the purple fabric needed is obtained as,

  $\begin{array}{c}A=\frac{1}{2}\left(4+4\right)\left(2+3\right)\\ =\frac{1}{2}\left(8\right)\left(5\right)\\ =20{\text{in}}^2\end{array}$

Thus, the area of red, orange, blue, green and blue colour each is $24{\text{in}}^2$ and the area of purple fabric needed is $20{\text{in}}^2$ .

(b)

To determine

To find: Whether the kit meet the requirements.

Answer to Problem 25PPS

The value $140{\text{in}}^2<200{\text{in}}^2$ , so the kite meets the requirements.

Explanation of Solution

Given:

The area of the kite should be no more than $200{\text{in}}^2$ .

Calculation:

Consider the total area of the kite required is the sum of area of all the fabric needed that is,

  $\begin{array}{c}A=5\left(24\right)+20\\ =120+20\\ =140{\text{in}}^2\end{array}$

Since, $140{\text{in}}^2<200{\text{in}}^2$ , the kite meets the requirements.