Question

What is the area of the regular trapezoid below?

A trapezoid has a base of 20 inches, height of 8 inches, and top side length of 12 inches.
128 Inches squared
160 Inches squared
960 Inches squared
1,920 Inches squared

Answer 1

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

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

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

In this trapezoid, the lengths of the bases are:

- \( b_1 = 20 \) inches (the longer base)
- \( b_2 = 12 \) inches (the shorter base)

And the height \( h = 8 \) inches.

Now, substituting these values into the formula:

\[
\text{Area} = \frac{1}{2} \times (20 + 12) \times 8
\]

Calculating \( (20 + 12) \):

\[
20 + 12 = 32
\]

Now, substitute this back into the area formula:

\[
\text{Area} = \frac{1}{2} \times 32 \times 8
\]

Calculating \( \frac{1}{2} \times 32 \):

\[
\frac{1}{2} \times 32 = 16
\]

Now, multiplying by the height:

\[
\text{Area} = 16 \times 8 = 128
\]

Thus, the area of the trapezoid is:

\[
\text{Area} = 128 \text{ square inches}
\]

Therefore, the answer is:

\(\boxed{128 \text{ inches squared}}\)