Question

Help (this for a friend)
a 62.1
b 117.4
c 122.1
d 164.5

Answer 1

C. 122.1

Explanation:

The area of a semicircle is HALF of the area of the circle. As the area of a circle is
`\pi r^2`. So, the area of a semicircle is
`(1)/(2)(\pi r^2)`, where r is the radius.

18 × 6

= 108

108
`cm^2` 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
`(1)/(2)(\pi r^2)` to find the area of the semicircle,

`(1)/(2) (\pi 3^2)`

(Remember pie is 3.14...)

Slove:

`\mathrm{Remove\:parentheses}:\quad \left(a\right)=a`

`=(1)/(2)\pi 3^2`

`\mathrm{Multiply\:fractions}:\quad \:a\cdot (b)/(c)=(a\:\cdot \:b)/(c)`

`=(1\pi 3^2)/(2)`

`\mathrm{Multiply:}\:1\pi =\pi`

`=(3^2\pi )/(2)`

`3^2=9`

`=(9\pi )/(2)`

`(9\pi )/(2) =\left(\mathrm{Decimal:\quad }\:14.13716\dots \right)`

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
`cm^2`. Answer ⇒ C.

Answer 2

c. 122.1 cm

Explanation:

so l * w +
`(\pi r^2)/(2)`

since 6 cm is the diameter

6/2 = 3

the radius (or r) is 3

so 18 * 6 +
`(3.14 * 3*3)/(y)`

108 +
`(3.14*9)/(y)`

108 +
`(28.26)/(2)`

108 + 14.13 = 122.13

simplified: 122.1 cm

hope this helps:)