Trapezoid Area Formula: Finding Height When Area = 20cm² and Base Sum = 10cm

The formula for the area of a trapezoid is given by:

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

where $A$ is the area, $b_1$ and $b_2$ are the lengths of the two bases, and $h$ is the height.

We are given:

• $A = 20 \, \text{cm}^2$
• $b_1 + b_2 = 10 \, \text{cm}$

We substitute these values into the formula:

$20 = \frac{1}{2} \times 10 \times h$

To find $h$, we simplify the equation:

$20 = 5h$

Dividing each side by 5, we get:

$h = \frac{20}{5}$

Hence, the height of the trapezoid is:

$h = 4 \, \text{cm}$

Therefore, the height of the trapezoid is 4 cm.