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

$A=\frac{1}{2}bh$

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:

$\text{Area}=\frac{1}{2}(12)(9)=\frac{108}{2}=54$

Area of rectangle is given by

$\text{Area}=length\times width=5\times4=20$

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