Answer:
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.
[tex]\begin{gathered} \text{Area of a square=}s^2 \\ \text{Area of Patio A}=12^2=144\text{ square yards} \end{gathered}[/tex]
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.
[tex]\begin{gathered} \text{Area of a square=}s^2 \\ \text{Area of Patio B}=6.1^2=37.21\text{ square yards} \end{gathered}[/tex]
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:
[tex]\begin{gathered} \text{Area of the hexagon=6}\times Area\text{ of one triangle} \\ =6\times\frac{1}{2}\times bh \\ =3\times12\times8 \\ =288\text{ square yards} \end{gathered}[/tex]
The area of the hexagon is 288 square yards.
Area of the Composite Figure:
[tex]\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}[/tex]
The area of the composite figure is 506.42 square yards.
