Question

Can someone please help me

Find the area of each shaded region.

Round the answer to two decimal places.

please show work

Answer 1

7) S=6.28 yd A=12.57
`yd^(2)`

8) S=99.48 ft A=945.1
`ft^(2)`

9) S=21.99 in A=43.98
`in^(2)`

Explanation:

7)

S=r θ

S=4(
`(90\pi )/(180)`)........................................plug in values

S=4(
`(\pi )/(2)`)...........................................simplify

S=6.28 yd...................................solve and round

A=
`(1)/(2)`(
`r^(2)`) θ

A=
`(1)/(2)`(
`4^(2)`)(
`(90\pi )/(180)`) ....................................plug in values

A=
`(1)/(2)`(16)(
`(\pi )/(2)`) .....................................simplify

A=12.57
`yd^(2)`...................................solve and round.

8)

S=r θ

S=19(
`(300\pi )/(180)`).........................................plug in values

S=19(
`(5\pi )/(3)`).............................................simplify

S=99.48 ft........................................solve and round

A=
`(1)/(2)`(
`r^(2)`) θ

A=
`(1)/(2)`(
`19^(2)`)(
`(300\pi )/(180)`) ....................................plug in values

A=
`(1)/(2)`(361)(
`(5\pi )/(3)`) .....................................simplify

A=945.1
`ft^(2)`.......................................solve and round.

9)

S=r θ

S=4(
`(315\pi )/(180)`) ............................................plug in values

S= 4(
`(7\pi )/(4)`)..............................................simplify

S=21.99 in..........................................solve and round

A=
`(1)/(2)`(
`r^(2)`)θ

A=
`(1)/(2)`(
`4^(2)`)(
`(315\pi )/(180)`) ....................................plug in values

A=
`(1)/(2)`(16)(
`(7\pi )/(4)`)......................................simplify

A=43.98
`in^(2)`....................................solve and round.