Question

Find the area of the shaded region if the dimensions of the unshaded region are 18ft x 22ft. Use 3.14 for π as necessary.

A. 1,419.84 ft²
B. 1,111.84 ft²
C. 709.92 ft²
D. 957.84 ft²

Answer 1

Answer is option B. 1,111.84 ft²

Explanation:

The given dimensions of the un shaded region or rectangle are 18 feet x 22 feet.

Now we have additional 7 feet at both ends to form the diameter of the semicircle, making it
`14+18=32` feet

Radius =
`(32)/(2)=16` feet

We have 2 semicircles, one at each end. If we combine it it forms a circle.

Area of the circle (2 semicircles) =
`\pi r^(2)`

=
`3.14*(16)^(2)` = 803.84 square feet

Now we will find the area of the shaded rectangles above and below the non shaded one. The length is 22 feet and width is 7 feet.

So, area =
`22*7=154` square feet

We have 2 similar rectangles. So, area of both =
`2*154=308` square feet

So, total area of shaded region =
`803.84+308=1111.84` square feet.

Answer 2

See the attached picture: