A trapezium has two parallel sides of lengths 5cm and 9cm. If the area is 91cm$^2$, find the distance between the parallel sides

1. Analyze the question

We are given a trapezium with:

• Length of the first parallel side ($a$) = 5 cm
• Length of the second parallel side ($b$) = 9 cm
• Area of the trapezium ($A$) = 91 cm$^2$
• We need to find the distance between the parallel sides, which is the height ($h$).

2. Explain the concept

The area of a trapezium is calculated using the formula:

Where:

• $a$ and $b$ are the lengths of the parallel sides.
• $h$ is the perpendicular distance (height) between the parallel sides.

3. Show the solution

Step 1: Substitute the known values into the formula.

Step 2: Simplify the expression inside the parentheses.

Step 3: Multiply $\frac{1}{2}$ by 14.

Step 4: Solve for $h$ by dividing both sides by 7.

4. Identify the answer

The distance between the parallel sides is 13 cm. This corresponds to option A.

5. Tip

When dealing with area problems for shapes like trapeziums, always remember the "average of the parallel sides multiplied by the height" rule. It makes the formula easier to remember: $Area = (\text{Average of parallel sides}) \times \text{height}$.