Question

4:58 PM 16 AA.18 Area of compound figures... < Surina Silva's prac... 38 What is the area of this figure? 3 mi 14 mi 5 mi 9 mi 10 mi 5 mi 4 mi 10 mi Write your answer using decimals, if necessary. square miles.

Answer 1

230 square miles

Step-by-step explanation

We can divide this figure as shown in the picture: 2 rectangles and a right triangle. We find the area of each figure and then we add them up.

One of the rectangles's length is 5 mi and its width is 14 mi. Its area is:

`A_{\text{rectangle}1}=5mi*14mi=70mi^2`

The other rectangle's lenght is 10mi and its width is 5mi. Its area is:

`A_{\text{rectangle}2}=10mi*5mi=50mi^2`

The triangle height is:

`3mi+5mi+10mi+4mi=22mi`

And its base is 10mi. Its area is:

`A_{\text{triangle}}=(22mi*10mi)/(2)=(220mi^2)/(2)=110mi^2`

The area of the figure is:

`\begin{gathered} A=A_{\text{rectangle}1}+A_{\text{rectangle}2}+A_{\text{triangle}} \\ A=70mi^2+50mi^2+110mi^2 \\ A=230mi^2 \end{gathered}`