How to Find the Area of a Trapezoid - Free Printable

Problem:

We are tasked with finding the area of a trapezoid. The given dimensions are:
- \( b_1 = 10 \) ft (length of the top base)
- \( b_2 = 18 \) ft (length of the bottom base)
- \( h = 17 \) ft (height of the trapezoid)
- \( l_1 = 17.7 \) ft (length of one non-parallel side)
- \( l_2 = 16.6 \) ft (length of the other non-parallel side)

The formula for the area of a trapezoid is:
\[
A = \frac{1}{2} (b_1 + b_2) h
\]

Step-by-Step Solution:

1. Identify the relevant formula:
The formula for the area of a trapezoid is:
\[
A = \frac{1}{2} (b_1 + b_2) h
\]
Here, \( b_1 \) and \( b_2 \) are the lengths of the two parallel bases, and \( h \) is the height of the trapezoid.

2. Substitute the given values into the formula:
- \( b_1 = 10 \) ft
- \( b_2 = 18 \) ft
- \( h = 17 \) ft

Plugging these values into the formula:
\[
A = \frac{1}{2} (10 + 18) \cdot 17
\]

3. Simplify the expression inside the parentheses:
\[
10 + 18 = 28
\]
So the formula becomes:
\[
A = \frac{1}{2} \cdot 28 \cdot 17
\]

4. Multiply \( \frac{1}{2} \) by 28:
\[
\frac{1}{2} \cdot 28 = 14
\]
Now the formula simplifies to:
\[
A = 14 \cdot 17
\]

5. Perform the multiplication:
\[
14 \cdot 17 = 238
\]

6. State the final answer:
The area of the trapezoid is:
\[
\boxed{238}
\]

Explanation:

- The formula for the area of a trapezoid is derived from the idea of averaging the lengths of the two parallel bases and multiplying by the height.
- The given values for \( b_1 \), \( b_2 \), and \( h \) are directly used in the formula.
- The lengths \( l_1 \) and \( l_2 \) (the non-parallel sides) are not needed to calculate the area, as the formula only requires the bases and the height.

Thus, the area of the trapezoid is \(\boxed{238}\) square feet.