Question

I have answers for these but I'm not sure if they are correct it will ask for:Area of hexagon:Area of patio A:Area of B patios:Area of composite:Find the area of the building and patios in the figure. All shapes in the composite figure are regular polygons.

Answer 1

506.42 square yards.

Explanation:

In the diagram, all the shapes are regular polygons.

Area of Patio A

Patio A is a square with side length, s = 12 yards.

`\begin{gathered} \text{Area of a square=}s^2 \\ \text{Area of Patio A}=12^2=144\text{ square yards} \end{gathered}`

The area of Patio A is 144 square yards.

Area of Patio B

Patio B is a square with side length, s = 6.1 yards.

`\begin{gathered} \text{Area of a square=}s^2 \\ \text{Area of Patio B}=6.1^2=37.21\text{ square yards} \end{gathered}`

The area of Patio B is 37.21 square yards.

Area of the Hexagon

A regular hexagon can be divided into 6 equilateral triangles.

In the diagram:

• The base of one equilateral triangle = 12 yards

,

• The height of one equilateral triangle = 8 yards

The area of the hexagon therefore is:

`\begin{gathered} \text{Area of the hexagon=6}* Area\text{ of one triangle} \\ =6*(1)/(2)* bh \\ =3*12*8 \\ =288\text{ square yards} \end{gathered}`

The area of the hexagon is 288 square yards.

Area of the Composite Figure:

`\begin{gathered} \text{Area}=\text{Area of Patio A+2(Area of Patio B})+\text{Area of Hexagon} \\ =144+2(37.21)+288 \\ =506.42\text{ square yards} \end{gathered}`

The area of the composite figure is 506.42 square yards.