A trapezium has an area of 150 square centimeters. If the lengths of its two parallel sides are 12 cm and 18 cm, what is the distance between these two parallel sides?

Question: A trapezium has an area of 150 square centimeters. If the lengths of its two parallel sides are 12 cm and 18 cm, what is the distance between these two parallel sides?

Solution:
Given,
Area of the trapezium, A = 150 cm²
Lengths of the parallel sides, a = 12 cm and b = 18 cm
Let the distance between the two parallel sides (height) = h cm

We know,
Area of a trapezium, A = 1/2 × (sum of parallel sides) × height
∴ 150 = (1/2) × (12 + 18) × h
⇒ 150 = (1/2) × 30 × h
⇒ 150 = 15 × h
⇒ h = 150 ÷ 15
∴ h = 10

∴ The height = 10 cm.