Chapter 13.1, Problem 24PSC

(a)

To determine

To find: The areas of regions I, II, and III.

Answer to Problem 24PSC

The areas of regions I, II, and III are $24$ , $10$ , and $15$ square unit, respectively.

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Find the area of the region I as follows.

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

Find the area of the region II as follows.

  $\begin{array}{c}{A}_{\text{II}}=\frac{1}{2}\left(4\right)\left(5\right)\\ =10\end{array}$

Find the area of the region III as follows.

  $\begin{array}{c}{A}_{\text{II}}=\frac{1}{2}\left(10\right)\left(3\right)\\ =15\end{array}$

Therefore, the areas of regions I, II, and III are $24$ , $10$ , and $15$ square unit, respectively.

(b)

To determine

To find: The area of $\text{ΔOBD}$ .

Answer to Problem 24PSC

The area of $\text{ΔOBD}$ is $31$ square unit.

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Find the area of the rectangle $\text{OACE}$ as follows.

  $\begin{array}{c}A=\left(10\right)\left(8\right)\\ =80\end{array}$

Find the area of $\text{ΔOBD}$ as follows.

  $\begin{array}{c}{A}_{\text{ΔOBD}}=80-\left(24+10+15\right)\\ =31\end{array}$

Therefore, the area of $\text{ΔOBD}$ is $31$ square unit.