Chapter 11.9, Problem 18PPS

a.

To determine

Todescribe:the irregular shape can be separated in to polygons and find its area.

Answer to Problem 18PPS

  $A=\frac{1}{2}\left(a+b\right)h$ .

Explanation of Solution

Given:

A diagram of the Denali national park wilderness area in Alaska is shown below:

  

Calculation:

Consider the figure,

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

The figure is a composite is rectangle and a trapezium.

Therefore, the area of the figure is sum of the area of the trapezium and rectangle.

Now, area of the trapezium is given by the formula is $A=\frac{1}{2}\left(a+b\right)h$

Where a and b are two bases.

Hence, area of the trapezium is $A=\frac{1}{2}\left(a+b\right)h$ .

b.

To determine

To estimate: the number of square miles contained in the Denali national park wilderness area.

Answer to Problem 18PPS

  $930\text{square}\text{mile }$ .

Explanation of Solution

Given:

  $y=10\text{unit}$

Calculation:

The objective is number of square miles contained in the Denali national park wilderness area.

Therefore, the area of the trapezium CDEF.

  $\begin{array}{l}A=\frac{1}{2}\left(a+b\right)h\\ =\frac{1}{2}\left(50+43\right)20\\ =10\times 93=930\text{square}\text{mile}\end{array}$

Hence, the number of square miles contained in the Denali national park wilderness area of is $930\text{square}\text{mile }$ .

c.

To determine

To estimate:the perimeter of the wildness area.

Answer to Problem 18PPS

  $1050\text{unit}$ .

Explanation of Solution

Given:

  $y=10\text{unit}$

Calculation:

The objective is to describe find the perimeter of the wildness area.

Therefore, the area of the trapezium CDEF.

Now, perimeter of the trapezium is given by the formula is

  $\begin{array}{l}P=\text{sum of four sides}\\ =CD+DE+FE+FC\\ =50+20+43+20\text{mile}\\ =133\text{mile}\end{array}$

Hence, the perimeter of the national park of is $133\text{mile}$ .