The trapezoid shown has an area of 1,575 sq cm. Which equation could you solve to find the height of the trapezoid?

To find the height of a trapezoid when you know its area, you can use the formula for the area of a trapezoid:

$A = \frac{1}{2} \times (b_1 + b_2) \times h$

where:

• $A$ is the area,
• $b_1$ and $b_2$ are the lengths of the two parallel sides (bases), and
• $h$ is the height.

Given the area $A = 1575 \, \text{sq cm}$, you can rearrange the formula to solve for the height $h$:

1. Start with the formula for the area of a trapezoid: $A = \frac{1}{2} \times (b_1 + b_2) \times h$

2. Substitute the known area into the equation: $1575 = \frac{1}{2} \times (b_1 + b_2) \times h$

3. To isolate $h$, multiply both sides by 2: $2 \times 1575 = (b_1 + b_2) \times h$ $3150 = (b_1 + b_2) \times h$

4. Finally, divide both sides by $(b_1 + b_2)$: $h = \frac{3150}{(b_1 + b_2)}$

Final Answer

The equation you could solve to find the height $h$ of the trapezoid is: $h = \frac{3150}{(b_1 + b_2)}$