Question

how can the area of a trapezoid formula be rearranged to find h?

Answer 1

The area \( A \) of a trapezoid can be calculated using the formula:

\[
A = \frac{1}{2} (b_1 + b_2) h
\]

where:
- \( A \) is the area,
- \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (bases),
- \( h \) is the height of the trapezoid.

To rearrange this formula to solve for \( h \), you can follow these steps:

1. Start with the area formula:
\[
A = \frac{1}{2} (b_1 + b_2) h
\]

2. Multiply both sides by 2 to eliminate the fraction:
\[
2A = (b_1 + b_2) h
\]

3. Now, divide both sides by \( (b_1 + b_2) \) to isolate \( h \):
\[
h = \frac{2A}{b_1 + b_2}
\]

Now you have the height \( h \) expressed in terms of the area \( A \) and the lengths of the two bases \( b_1 \) and \( b_2 \):

\[
h = \frac{2A}{b_1 + b_2}
\]