Question

Use the formula for area of a trapezoid to find the area of the trapezoid 13 in 14 in 15 in 32 in A 299 in B 598 in C 345 in D 182 in

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

From the dimensions you've provided, it appears that the two bases of the trapezoid are 13 inches and 32 inches, and the height is 14 inches. The value of 15 inches could be extraneous or misclassified in the question.

Plugging the values into the formula:

\[
b_1 = 13 \text{ in}
\]
\[
b_2 = 32 \text{ in}
\]
\[
h = 14 \text{ in}
\]

Now substitute these values into the formula:

\[
\text{Area} = \frac{1}{2} \times (13 + 32) \times 14
\]

Calculate \( 13 + 32 \):

\[
13 + 32 = 45
\]

Now substitute that back into the area formula:

\[
\text{Area} = \frac{1}{2} \times 45 \times 14
\]

Calculate \( 45 \times 14 \):

\[
45 \times 14 = 630
\]

Then divide by 2:

\[
\text{Area} = \frac{630}{2} = 315
\]

Given that 315 is not an option, if instead the base lengths provided were different interpretations, please clarify, or use:

The trapezoids with bases of 15 in and 32 in and a height of 14 in.

For these dimensions:

\[
b_1 = 15 \text{ in}
\]
\[
b_2 = 32 \text{ in}
\]
\[
h = 14 \text{ in}
\]

Inserting in formula,

\[
\text{Area} = \frac{1}{2} \times (15 + 32) \times 14
\]
\[
= \frac{1}{2} \times 47 \times 14
\]
\[
= \frac{658}{2} = 329
\]

Please let me know if further adjustments are required with the dimensions provided.