The problem states that the length of the middle base of a trapezium is 15 cm and the height is 8 cm. We need to find the area of the trapezium.

1. Problem Description

The problem states that the length of the middle base of a trapezium is 15 cm and the height is 8 cm. We need to find the area of the trapezium.

2. Solution Steps

The area of a trapezium is given by the formula:

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

where $a$ and $b$ are the lengths of the parallel sides (bases) and $h$ is the height.

The "middle base" of a trapezium is the line segment connecting the midpoints of the non-parallel sides. Its length is equal to the average of the lengths of the two parallel sides. Let the length of the middle base be $m$. Then,

$m = \frac{a + b}{2}$

We are given that $m = 15$ cm and $h = 8$ cm. We can rewrite the area formula as:

$Area = (\frac{a + b}{2}) h = m h$

Plugging in the given values:

$Area = 15 \times 8$

$Area = 120$

3. Final Answer

The area of the trapezium is 120 cm$^2$. Therefore, the answer is B.

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