Answer:
C. 122.1
Step-by-step explanation:
The area of a semicircle is HALF of the area of the circle. As the area of a circle is [tex]\pi r^2[/tex]. So, the area of a semicircle is [tex]\frac{1}{2}(\pi r^2)[/tex], where r is the radius.
18 × 6
= 108
108 [tex]cm^2[/tex] is the area of the rectangle,
For the semicircle, we know the diameter is equal to 6 cm,
(Remember that Diameter is equal to the radius times 2 (r × 2)),
To find the radius, divide the diameter by 2,
6 ÷ 2
= 3
The radius of the semicircle is 3 cm
Now use the equation [tex]\frac{1}{2}(\pi r^2)[/tex] to find the area of the semicircle,
[tex]\frac{1}{2} (\pi 3^2)[/tex]
(Remember pie is 3.14...)
Slove:
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]
[tex]=\frac{1}{2}\pi 3^2[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
[tex]=\frac{1\pi 3^2}{2}[/tex]
[tex]\mathrm{Multiply:}\:1\pi =\pi[/tex]
[tex]=\frac{3^2\pi }{2}[/tex]
[tex]3^2=9[/tex]
[tex]=\frac{9\pi }{2}[/tex]
[tex]\frac{9\pi }{2} =\left(\mathrm{Decimal:\quad }\:14.13716\dots \right)[/tex]
Now take the decimal 14.13716.... and round to the nearest tenth,
14.13
(Remember 4 or less keep it the same, 5 or more bring the value up one more)
3 less than 5 so keep the 1 the same,
14.1
Now add 108 and 14.1,
108 + 14.1
= 122.1
Therefore the total area of the shape is 122.1 [tex]cm^2[/tex]. Answer ⇒ C.
