A trapezium has an area of 45 square inches and a height of 5 inches. Find the length
of its middle base.

Question

A trapezium has an area of 45 square inches and a height of 5 inches. Find the length of its middle base.

UpStudy AI · Accepted Answer

Let the lengths of the two parallel sides of the trapezium be $$b_1$$ and $$b_2$$. The middle base (or mid-segment) of a trapezium is the average of these two lengths:

$$
m = \frac{b_1 + b_2}{2}
$$

The area $$A$$ of a trapezium is given by:

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

Since the mid-segment is $$\frac{b_1 + b_2}{2}$$, we can rewrite the area formula as:

$$
A = m \times h
$$

We are given:
$$
A = 45\ \text{square inches} \quad \text{and} \quad h = 5\ \text{inches}
$$

Substitute these values into the formula:

$$
45 = m \times 5
$$

Solve for $$m$$:

$$
m = \frac{45}{5} = 9
$$

Thus, the length of the middle base is $$\boxed{9\ \text{inches}}$$.
The length of the middle base is 9 inches.

A trapezium has an area of 45 square inches and a height of 5 inches. Find the length
of its middle base.

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