Question

I’m stuck on this problem hope someone could help not a test just simple work sheet

Answer 1

The figure is the composition of two other figures:

• a square of size L = 12ft,

,

• a semi-circle of diameter d = 12ft.

The total area of the figure is equal to the sum of the areas of each subfigure:

`A_{\text{Total}}=A_{\text{Square}}+A_{\text{Semi}-\text{circle}}\text{.}`

The area of the square is:

`A_{\text{Square}}=L^2=(12ft)^2=144ft^2.`

The area of the semi-circle is half the area of a circle of the same diameter:

`A_{\text{Semi}-\text{circle}}=(1)/(2)\cdot A_{\text{Circle}}=(1)/(2)\cdot(1)/(4)\pi d^2=(1)/(8)\cdot\pi\cdot(12ft)^2=18\pi ft^2\cong56.5ft^2.`

Summing the areas, we get:

`A_{\text{Total}}\cong144ft^2+56.5ft^2=200.5ft^2.`

Answer

E) 200.5ft²