Question

A semicircle is attached to the side of a rectangle as shown.

What is the best approximation for the area of this figure?

Use 3.14 to approximate pi.

Answer 1

`58.8\ mm^(2)`

Explanation:

we know that

The area of the figure is equal to the area of a rectangle plus the area of semicircle

Step 1

Find the area of the rectangle

The area of the rectangle is equal to

`A=bh`

we have

`b=9\ mm`

`h=3\ mm`

substitute

`A=9*3=27\ mm^(2)`

Step 2

Find the area of semicircle

The area of semicircle is equal to

`A=(1)/(2)\pi r^(2)`

we have

`r=9/2=4.5\ m`

substitute

`A=(1)/(2)(3.14)(4.5^(2))=31.8\ mm^(2)`

Step 3

Find the area of the figure

`27\ mm^(2)+31.8\ mm^(2)=58.8\ mm^(2)`