Question

GEOMEIRY the formula for the area of a trapezoid is $A=\frac{1}{2}h\left(a+b\right)$,where $h$represents the height and $a$ and $b$represent the lengths of the bases. Solve for $h$.

Short answer

The formula for the area the trapezoid for the height$h$ is $\frac{2A}{\left(a+b\right)}$.

Step-by-step solution

Step 1. Given information.

The formula for the area of the trapezoid:

$\begin{array}{l}A=\frac{1}{2}h\left(a+b\right)\\ \text{where,}\\ h=\text{height,}a\text{and}b\text{arethelengthsofthebases}\end{array}$

Step 2. Calculation.

Solve the formula for the area the trapezoid for $h$:

role="math" localid="1643107414025" $\begin{array}{l}A=\frac{1}{2}h\left(a+b\right)\\ \Rightarrow 2A=h\left(a+b\right)\\ \Rightarrow h=\frac{2A}{\left(a+b\right)}\end{array}$

Step 3. Conclusion.

Hence, the formula for the area the trapezoid for the height$h$ is $\frac{2A}{\left(a+b\right)}$.