We are given a trapezium with height 12 cm and parallel sides $b$ cm and $4b$ cm. The area of the trapezium is 120 $cm^2$. We need to find the value of $b$.

1. Problem Description

We are given a trapezium with height 12 cm and parallel sides $b$ cm and $4b$ cm. The area of the trapezium is 120 $cm^2$. We need to find the value of $b$.

2. Solution Steps

The area of a trapezium is given by the formula:

$Area = \frac{1}{2} \times height \times (sum\ of\ parallel\ sides)$

In this case, the area is 120, the height is 12, and the parallel sides are $b$ and $4b$. Plugging these values into the formula, we get:

$120 = \frac{1}{2} \times 12 \times (b + 4b)$

Simplifying the equation:

$120 = 6 \times (5b)$

$120 = 30b$

To find the value of $b$, we divide both sides of the equation by 30:

$b = \frac{120}{30}$

$b = 4$

3. Final Answer

The value of $b$ is 4.