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.

Select from the drop-down menu to correctly complete the statement.

Answer 1

`58.8\ mm^2`

Explanation:

we know that

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

step 1

Find the area of rectangle

The area of rectangle is equal to

`A=bh`

where

`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\ mm` ---> the radius is half the diameter

`\pi =3.14`

substitute

`A=(1)/(2)(3.14) (4.5)^(2)`

`A=31.8\ mm^2`

step 3

Find the area of the figure

`A=27+31.8=58.8\ mm^2`