Calculate Trapezoid Height: Area 20 cm² with 10 cm Base Sum

To solve this problem, we'll use the trapezoid area formula:

Given:

• Area, $S = 20 \, \text{cm}^2$
• Sum of bases, $b_1 + b_2 = 10 \, \text{cm}$

The formula for the area of a trapezoid is:

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

Substituting the known values into the formula, we have:

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

Simplifying the equation:

$20 = 5 \times h$

Solving for $h$, we divide both sides by 5:

$h = \frac{20}{5} = 4 \, \text{cm}$

Therefore, the height of the trapezoid is $4 \, \text{cm}$.