Question

Need help please area shaded regions measurments!!

Answer 1

83.37
`in^(2)`

Explanation:

We need to find the area of the trapezoid and then subtract out the area of the half circle.

Trapezoid

a =
`(a+b)/(2)`(h)

The a and the b are the lengths of the top and bottom of the trapezoid. The h is the height.

a =
`(10+16)/(2)`(7.5) I get the 16 from the bottom. 5 + 5 + 3 + 3. The radius of the circle doubled gives us the bottom of the circle.

a = 13(7.5)

a = 97.5

97.5 is the area of the whole trapezoid. We need to subtract out the half circle that is not shaded.

Circle

a =
`(\pi r^(2) )/(2)` we are dividing by 2, because it is half of a circle. I am going to use 3.14 for
`\pi`

a =
`((3.14)3^(2) )/(2)`

a =
`(3.14(9))/(2)`

a =
`(28.26)/(2)`

a = 14.13

97.5 - 14.13 = 83.37

Helping in the name of Jesus.