Question
Which correctly shows the area formula for a trapezoid a equals 1/2 height B1 + B2 rearrange for the quantity of interest h
Answers
GPT-4o mini
The area \( A \) of a trapezoid can be expressed using the formula:
\[
A = \frac{1}{2} h (B_1 + B_2)
\]
where:
- \( A \) is the area,
- \( h \) is the height,
- \( B_1 \) and \( B_2 \) are the lengths of the two parallel sides.
To rearrange this formula to solve for the height \( h \), follow these steps:
1. Multiply both sides by 2 to eliminate the fraction:
\[
2A = h (B_1 + B_2)
\]
2. Now, divide both sides by \( (B_1 + B_2) \) to isolate \( h \):
\[
h = \frac{2A}{B_1 + B_2}
\]
Thus, the rearranged formula for the height \( h \) of a trapezoid in terms of its area \( A \) and the lengths of the bases \( B_1 \) and \( B_2 \) is:
\[
h = \frac{2A}{B_1 + B_2}
\]
\[
A = \frac{1}{2} h (B_1 + B_2)
\]
where:
- \( A \) is the area,
- \( h \) is the height,
- \( B_1 \) and \( B_2 \) are the lengths of the two parallel sides.
To rearrange this formula to solve for the height \( h \), follow these steps:
1. Multiply both sides by 2 to eliminate the fraction:
\[
2A = h (B_1 + B_2)
\]
2. Now, divide both sides by \( (B_1 + B_2) \) to isolate \( h \):
\[
h = \frac{2A}{B_1 + B_2}
\]
Thus, the rearranged formula for the height \( h \) of a trapezoid in terms of its area \( A \) and the lengths of the bases \( B_1 \) and \( B_2 \) is:
\[
h = \frac{2A}{B_1 + B_2}
\]