Question

Find the a area and b perimeter of the figure. Dimensions are in feet.

Answer 1

a. Area

The area of the figure is the sum of the area of the rectangle and the area of the triangle. Therefore:

Area of triangle is given by

`A=(1)/(2)bh`

First, we find the height of the triangle using the Pythagorean theorem:

`\begin{gathered} h^2+b^2=c^2 \\ h^2+12^2=(10+5)^2 \\ h^2+144=225 \\ h^2+144-144=225-144 \\ h^2=81 \\ h=\sqrt[]{81} \\ h=9 \end{gathered}`

So, the area is:

`\text{Area}=(1)/(2)(12)(9)=(108)/(2)=54`

Area of rectangle is given by

`\text{Area}=length* width=5*4=20`

The area of the figure is:

`\text{Area of figure=54+20=}74`

Answer: area = 74 ft^2

b. Perimeter

Perimeter is the sum of all sides, therefore:

`\text{Perimeter}=10+4+5+4+12+9=44`

Answer: perimeter = 44 ft