Chapter 11.9, Problem 22PPS

a.

To determine

Todescribe:the geometric figurewhose area is find.

Answer to Problem 22PPS

Area of the figure is sum of the area of the triangle, plus the sum of the area of the rectangle.

Explanation of Solution

Given:

Aninvestigation of area of composite figure is shown below:

  

Calculation:

Consider the figure,

The objective is to describe the figure.

The figure is a combination of a rectangle and a triangle.

therefore, the area of the figure is sum of the area of the triangle, plus the sum of the area of the rectangle.

b.

To determine

To list: the formula that is used to find the area of composite figure.

Answer to Problem 22PPS

  $159.9c{m}^2$ .

Explanation of Solution

Given:

An investigation of area of composite figure is shown below:

  

Calculation:

Consider the figure,

The objective is to find the area of the figure.

The area Aof rectangle is $A=l\times w$ andarea of triangle is $A=\frac{1}{2}\left(b\right)\left(h\right)$ .

Therefore, area of rectangle is $A=l\times w=7cm\times 16.4cm=114.8c{m}^2$ .

And the area of the triangle is $A=\frac{1}{2}\left(b\right)\left(h\right)=\frac{1}{2}\left(16.4\right)\left(5.5\right)=8.2\left(5.5\right)=45.1c{m}^2$ .

Therefore, the area of the figure is

  $\begin{array}{l}\text{Area of figure}=\text{sum of area of rectangle}+\text{ares of triangle}\\ A=114.8c{m}^2+45.8c{m}^2=159.9c{m}^2\end{array}$

Hence, the area of the figure is $159.9c{m}^2$ .

c.

To determine

To make:a conjecture about how the area of the composite figure change if its dimensions are doubled.

Answer to Problem 22PPS

  $639.6c{m}^2$ .

Explanation of Solution

Given:

The dimensions of rectangle are $l=2\times 16.4=32.8cm,w=2\times 7=14cm$

And the dimensions of triangle is $b=2\times 16.4=32.8\text{cm},h=2\times 5.5=11\text{cm}$ .

Calculation:

The objective is to describe find the area of composite figure.

The area A of rectangle is $A=l\times w$ and area of triangle is $A=\frac{1}{2}\left(b\right)\left(h\right)$ .

Therefore, area of rectangle is $A=l\times w=14cm\times 32.8cm=459.2c{m}^2$ .

And the area of the triangle is $A=\frac{1}{2}\left(b\right)\left(h\right)=\frac{1}{2}\left(32.8\right)\left(11\right)=16.4\left(11\right)=180.4c{m}^2$ .

Therefore, the area of the figure is

  $\begin{array}{l}\text{Area of figure}=\text{sum of area of rectangle}+\text{ares of triangle}\\ A=459.2c{m}^2+180.4c{m}^2=639.6c{m}^2\end{array}$

Hence, the area of the figure is $639.6c{m}^2$ .