Question

Cecilia made an envelope to mail a letter. She colored the regular trapezoid flap on the bottom of the envelope blue, as shown.

A trapezoid has a base of 9 inches, height of 2 inches, and top side length of 5 inches.

What is the area of the blue flap of the envelope?
14 Inches squared
18 Inches squared
45 Inches squared
90 Inches squared

Answer 1

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

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

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

In this case:
- \( b_1 = 9 \) inches (the length of the bottom base)
- \( b_2 = 5 \) inches (the length of the top base)
- \( h = 2 \) inches (the height)

Now substituting these values into the formula:

\[
\text{Area} = \frac{1}{2} \times (9 + 5) \times 2
\]
\[
= \frac{1}{2} \times 14 \times 2
\]
\[
= \frac{1}{2} \times 28
\]
\[
= 14 \text{ square inches}
\]

Thus, the area of the blue flap of the envelope is \( \boxed{14} \) square inches.