Trapezoid Length Calculation: Finding BC When Area is 100 cm²

We'll begin by using the formula for the area of a trapezoid:

$A = \frac{1}{2} \times (a + b) \times h$

where:

• $A$ is the area of the trapezoid, which is 100 cm².
• $a$ is the length of base AD, which is 15 cm.
• $b$ is the length of base BC, which we need to find.
• $h$ is the height of the trapezoid, which is 8 cm.

Substituting the known values into the formula, we have:

$100 = \frac{1}{2} \times (15 + b) \times 8$

First, simplify the right side of the equation:

$100 = 4 \times (15 + b)$

Next, divide both sides by 4 to isolate the terms inside the parenthesis:

$25 = 15 + b$

Finally, subtract 15 from both sides to solve for $b$:

$b = 25 - 15 = 10$

Therefore, the length of base BC is $\mathbf{10}$ cm.

The solution to the problem is $\boxed{10}$.