Question

What is the area of the trapezoid in square feet?
With the width of 52 ft the height of 40 ft the width at the top of the trapezoid is 32 ft.
_______ft^2

Answer 1

To find the area of a trapezoid, you can use the formula:

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

where \( b_1 \) is the length of the bottom base, \( b_2 \) is the length of the top base, and \( h \) is the height.

In your case:
- The bottom base \( b_1 = 52 \, \text{ft} \)
- The top base \( b_2 = 32 \, \text{ft} \)
- The height \( h = 40 \, \text{ft} \)

Now, plug these values into the formula:

\[
\text{Area} = \frac{1}{2} \times (52 + 32) \times 40
\]

Calculating inside the parentheses first:

\[
52 + 32 = 84
\]

Now, substitute that back into the formula:

\[
\text{Area} = \frac{1}{2} \times 84 \times 40
\]

Now compute:

\[
\frac{1}{2} \times 84 = 42
\]

Next, multiply \( 42 \) by \( 40 \):

\[
42 \times 40 = 1680
\]

Thus, the area of the trapezoid is:

\[
\text{Area} = 1680 \, \text{ft}^2
\]

So the final answer is:

\[
\boxed{1680 \, \text{ft}^2}
\]