Chapter 12.3, Problem 18IP

(a)

To determine

To describe: The way to separate the irregular shape into polygons to determine its area.

Answer to Problem 18IP

The irregular shape can be separated into two trapezoids to determine its area.

Explanation of Solution

Given information:

Consider the given shape of Park D in Country A.

  

Calculation:

In the given shape, the shape can be divided into two trapezoids. The first trapezoid is on the lower side and it has base lengths 110 miles and 45 miles with height 33 miles. The second trapezoid is on the top side and it has base lengths 43 miles and 50 miles with height 20 miles.

Conclusion:

Therefore, the irregular shape can be separated into two trapezoids to determine its area.

(b)

To determine

To find: The area of the Park D in Country A.

Answer to Problem 18IP

The area of the Park D in Country A is $3487.5{\text{mi}}^2$ .

Explanation of Solution

Given information:

Consider the given shape of Park D in Country A.

  

Calculation:

Write the expression to calculate the area of the lower trapezoid.

  ${\text{Area}}_1=\frac{1}{2}\left(b_1+b_2\right)h_1$

Where,

• $b_1$ is the base length of lower trapezoid.
• $b_2$ is the base length of lower trapezoid.
• $h_1$ is the height of lower trapezoid.

Substitute the values in the above expression.

  $\begin{array}{c}{\text{Area}}_1=\frac{1}{2}\left(45+110\right)\cdot 33\\ =2557.5{\text{mi}}^2\end{array}$

Write the expression to calculate the area of the upper trapezoid.

  ${\text{Area}}_2=\frac{1}{2}\left(b_3+b_4\right)h_2$

Where,

• $b_3$ is the base length of upper trapezoid.
• $b_4$ is the base length of upper trapezoid.
• $h_2$ is the height of upper trapezoid.

Substitute the values in the above expression.

  $\begin{array}{c}{\text{Area}}_2=\frac{1}{2}\left(43+50\right)\cdot 20\\ =930{\text{mi}}^2\end{array}$

Calculate the total area of Park D.

  $\begin{array}{c}\text{Total}\text{area}={\text{Area}}_1+{\text{Area}}_2\\ =2557.5+930\\ =3487.5{\text{mi}}^2\end{array}$

Conclusion:

Therefore, the area of the Park D in Country A is $3487.5{\text{mi}}^2$ .

(c)

To determine

To find: The perimeter of the Park D.

Answer to Problem 18IP

The perimeter of the Park D is 271 miles.

Explanation of Solution

Given information:

Consider the given shape of Park D in Country A.

  

Calculation:

Perimeter is the measure of the outside of the park. Calculate the perimeter of the Park D.

  $\begin{array}{c}\text{Perimeter}=20+43+20+110+33+45\\ =271\text{mi}\end{array}$

Conclusion:

Therefore, the perimeter of the Park D is 271 miles.