Question

Rearranging the formula for the area of a trapezoid to solve for 'h'

Answer 1

The formula for the area \( A \) of a trapezoid is given by:

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

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

To solve for \( h \), you can rearrange the formula as follows:

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

So, the height \( h \) of the trapezoid can be expressed as:

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