Question
Find the area of trapezoid QRST. Round your answer to the nearest tenth if necessary.
Q
R
S
T
26.4 in
22.1 in
7.2 in
14.6 in
14.4 in
Q
R
S
T
26.4 in
22.1 in
7.2 in
14.6 in
14.4 in
Answers
GPT-4o mini
To find the area of trapezoid QRST, we need to first recall the formula for the area \( A \) of a trapezoid:
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where:
- \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (bases),
- \( h \) is the height (the perpendicular distance) between the two bases.
Since the dimensions you provided seem to include multiple values (26.4 in, 22.1 in, 7.2 in, 14.6 in, 14.4 in), it’s not clear which correspond to the bases and which may correspond to the height. In trapezoids, we generally only need two bases and the height.
Assuming one of the sets is for the bases and the others are height, please clarify which dimensions correspond to the bases and which correspond to the height.
However, to illustrate how you would use the formula with hypothetical bases and height, let’s assume:
- \( b_1 = 26.4 \text{ in} \) (one base)
- \( b_2 = 22.1 \text{ in} \) (the other base)
- \( h = 7.2 \text{ in} \) (the height)
Plugging these values into the formula:
\[
A = \frac{1}{2} \times (26.4 + 22.1) \times 7.2
\]
\[
A = \frac{1}{2} \times 48.5 \times 7.2
\]
\[
A = 24.25 \times 7.2
\]
\[
A = 174.6 \text{ in}^2
\]
After calculating with these assumptions, round the answer if necessary. Based on our values and method:
The area of trapezoid QRST is approximately \( 174.6 \text{ in}^2 \).
If the bases and heights are different, just let me know the correct assignments, and I can adjust the calculations accordingly!
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where:
- \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (bases),
- \( h \) is the height (the perpendicular distance) between the two bases.
Since the dimensions you provided seem to include multiple values (26.4 in, 22.1 in, 7.2 in, 14.6 in, 14.4 in), it’s not clear which correspond to the bases and which may correspond to the height. In trapezoids, we generally only need two bases and the height.
Assuming one of the sets is for the bases and the others are height, please clarify which dimensions correspond to the bases and which correspond to the height.
However, to illustrate how you would use the formula with hypothetical bases and height, let’s assume:
- \( b_1 = 26.4 \text{ in} \) (one base)
- \( b_2 = 22.1 \text{ in} \) (the other base)
- \( h = 7.2 \text{ in} \) (the height)
Plugging these values into the formula:
\[
A = \frac{1}{2} \times (26.4 + 22.1) \times 7.2
\]
\[
A = \frac{1}{2} \times 48.5 \times 7.2
\]
\[
A = 24.25 \times 7.2
\]
\[
A = 174.6 \text{ in}^2
\]
After calculating with these assumptions, round the answer if necessary. Based on our values and method:
The area of trapezoid QRST is approximately \( 174.6 \text{ in}^2 \).
If the bases and heights are different, just let me know the correct assignments, and I can adjust the calculations accordingly!