Question

A swing set is going to be placed over a region of mulch that is shaped like a trapezoid. The bases of the trapezoid have a length of 12 and 15 feet, and the perpendicular distance between the bases is 8.5 feet. What is the area of the region under the swing set? If necessary, round your answer to the nearest tenth.

The area is ________ square feet.

Answer 1

114.8 square ft

Explanation:

We want to find the area of the mulch under the swing set, which is in the shape of a trapezoid.

The area of a trapezoid is denoted by:
`A=((b_1+b_2)*h)/(2)`, where
`b_1` and
`b_2` are the bases and h is the height.

Here, the two bases are 12 and 15, while the height is 8.5 ft. Plug in these values:

`A=((b_1+b_2)*h)/(2)`

`A=((12+15)*8.5)/(2)=114.75` ≈ 114.8 square ft

Answer 2

114.8\ ft^{2}

Explanation:

The area of a trapezoid is equal to A=\frac{1}{2}(b1+b2)h

In this problem we have

b1=12\ ft

b2=15\ ft

h=8.5\ ft ----> the height of the trapezoid is the perpendicular distance between the bases

substitute the values

A=\frac{1}{2}(12+15)(8.5)

A=\frac{1}{2}(27)(8.5)=114.75\ ft^{2}

Round to the nearest tenth

114.75=114.8\ ft^{2}