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.
The area is
A 62.1 cm²
B 117.4 cm²
C 122.1 cm²
D 164.5 cm²

Answer 1

Option C
`122.1\ cm^(2)`

Explanation:

we know that

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

see the attached figure to better understand the problem

Step 1

Find the area of the rectangle

The area of the rectangle is equal to

`A=bh`

we have

`b=18\ cm`

`h=6\ cm`

substitute

`A=18*6=108\ cm^(2)`

Step 2

Find the area of semicircle

The area of semicircle is equal to

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

we have

`r=6/2=3\ m`

substitute

`A=(1)/(2)(3.14)(3^(2))=14.1\ cm^(2)`

Step 3

Find the area of the figure

`108\ cm^(2)+14.1\ cm^(2)=122.1\ cm^(2)`