Question

A semicircle and square are put together to build a giant chair. The radius of the circle is 6 meters and each side of the square is 12 meters. What is the area of the back of the chair?

Answer 1

$$Area(semi-circle)$$Let's begin by listing out the information given to us:

This is a composite shape composed of a semicircle and a square

Radius (r) = 6 m

Length (l) = 12 m

To obtain the area of the composite shape, we will sum up the areas of the semicircle and square

AREA OF SEMI-CIRCLE

`\begin{gathered} Area(semi-circle)=(1)/(2)\pi r^2 \\ Area(semi-circle)=(1)/(2)\cdot3.14\cdot6^2 \\ Area(semi-circle)=56.52m^2 \end{gathered}`

AREA OF SQUARE

`\begin{gathered} AreaSquare=l^(2) \\ AreaSquare=12^(2)=144 \\ AreaSquare=144m^(2) \end{gathered}`

Total Area = Area of semicircle + Area of square = 56.52 + 144 = 200.52

Total Area = 200.52 m²