Question

Finding the area of unusual shapes

Answer 1

The shape in question is a composite shape.

It comprises two(2) shapes which are a triangle and a semi-circle.

The area of the shape is the sum of the area of the triangle and that of the semi-circle

The area of the triangle is:

`A_(triangle)=(1)/(2)* base* height`
`\begin{gathered} \text{Base of the triangle =}6\text{ yard} \\ Height\text{ of the triangle= 4 yard} \end{gathered}`

Thus,

`\begin{gathered} A_(triangle)=(1)/(2)*6*4 \\ A_(triangle)=12\text{ yards} \end{gathered}`

Area of the Semi-circle is:

`A_(semi-circle)=(\pi* r^2)/(2)`
`\begin{gathered} \text{Diameter of the circle=6 yard} \\ \text{Radius}=(Diameter)/(2) \\ \text{Radius}=(6)/(2)=3\text{ yard} \end{gathered}`
`\begin{gathered} A_(semi-circle)=(3.14*3^2)/(2) \\ A_(semi-circle)=(28.26)/(2) \\ A_(semi-circle)=14.13\text{ yard} \end{gathered}`

Hence, the area of the composite shape is:

`\begin{gathered} \text{Area of the triangle + Area of the semi-circle} \\ 12+14.13=26.13\text{ yard} \end{gathered}`