Question

I need help with this question for my exam practice, please.

Answer 1

Given the figure, the area of the rectangle is:

`A_{\text{rectangle}}=6\cdot9=54cm^2`

Now, we need to subtract the areas of the semicircles from this. The areas of the semicircles are:

`\begin{gathered} A_1=\pi\cdot(2^2)/(2)=2\pi cm^2 \\ A_2=\pi\cdot(2.5^2)/(2)=(25\pi)/(8)cm^2 \\ A_3=\pi\cdot(2.5^2)/(2)=(25\pi)/(8)cm^2 \end{gathered}`

Then, the area of the figure is:

`A=A_{\text{rectangle}}-A_1-A_2-A_3_{}_{}`

Using the values of each area:

`\begin{gathered} A=54-2\pi-(25\pi)/(8)-(25\pi)/(8)=(54-(33\pi)/(4))cm^2 \\ \Rightarrow A\approx28.082cm^2 \end{gathered}`