Question

3) 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 cm².

A) 62.1
B) 117.4
C) 122.1
D) 164.5

Please see attached photo. Thanks

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

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)`

Answer 2

Rectangle = 18 x 6 = 108
Circle: 3.14 x (3)^2 = 3.14 x 9 = 28.26
semicircle: 28.26 / 2 = 14.13

108 + 14.13 = 122.13

answer
122.13 cm^2