The lengths of the parallel sides of a trapezium are 9cm and 12cm. If the area of the trapezium is 105cm ^2…

Analyze the question: We are given a trapezium with parallel sides 9 cm and 12 cm and an area of 105 cm². We need the perpendicular height (the distance 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: 105 = ½ × (9 + 12) × h
2. Add the parallel sides: 105 = ½ × 21 × h
3. Multiply both sides by 2: 210 = 21h
4. Divide by 21: h = 210 ÷ 21 = 10

So the perpendicular distance is 10 cm.

Check: ½ × (9 + 12) × 10 = ½ × 21 × 10 = 105 cm² ✓

Tip: In trapezium questions, first find the sum of the parallel sides, then use "Area × 2 ÷ (sum of parallel sides)" to get the height directly: 105 × 2 ÷ 21 = 10. Always check by substituting your answer back into the formula.