Question

The backyard of a new home is shaped like a trapezoid with a height of 50 ft and bases of 77 ft and 113 ft. What is the cost of putting sod on the​ yard, if the landscaper charges ​$0.25 per square foot for​ sod?

Answer 1

To find the cost of putting sod on the backyard, we need to first calculate the area of the trapezoid, and then multiply that area by the cost per square foot of sod.

The area \( A \) of a trapezoid can be calculated using the formula:

\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]

where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.

Given:
- \( b_1 = 77 \) ft
- \( b_2 = 113 \) ft
- \( h = 50 \) ft

Now, plug in the values into the formula:

\[
A = \frac{1}{2} \times (77 + 113) \times 50
\]
\[
A = \frac{1}{2} \times 190 \times 50
\]
\[
A = 95 \times 50
\]
\[
A = 4750 \text{ square feet}
\]

Next, to find the total cost of putting sod in the yard, multiply the area by the cost per square foot:

\[
\text{Cost} = \text{Area} \times \text{Cost per square foot}
\]
\[
\text{Cost} = 4750 \times 0.25
\]
\[
\text{Cost} = 1187.50
\]

Therefore, the cost of putting sod on the yard is **$1187.50**.