The parallel sides of a trapezium are 13cm and 7cm. If the area of the trapezium is 50cm2, find the perpendicular distance between the parallel sides.

Analyze the question: We're given a trapezium with parallel sides 13 cm and 7 cm and an area of 50 cm². We need the perpendicular distance (height) between the parallel sides.

Concept: The area of a trapezium is

Area = ½ × (sum of parallel sides) × height

A = ½(a + b)h

Solution:

1. Substitute the values: 50 = ½ × (13 + 7) × h

2. Add the parallel sides: 50 = ½ × 20 × h

3. Simplify: 50 = 10h

4. Solve for h: h = 50 ÷ 10 = 5 cm

Check: ½ × (13 + 7) × 5 = ½ × 20 × 5 = 50 cm² ✔

Tip: In trapezium questions, add the parallel sides first. Here ½ × 20 = 10 immediately, so the area is just 10 × h. Always check your answer by substituting it back into the formula.