The distance between parallel sides of a trapezium is 12 cm and the distance between mid-points of other sides is 18 cm. Find the area of the trapezium.

Let ABCD be the trapezium in which AB || DC. Let E and F be mid-points of sides AD and BC respectively, then EF = 18 cm.

Given,

Distance between parallel sides of a trapezium is 12 cm.

∴ Height = 12 cm.

By formula,

Sum of the lengths of two parallel sides = 2 × Distance between mid-points of two non-parallel sides

⇒ AB + CD = 2 × EF = 2 × 18 = 36 cm.

Area of trapezium = $\dfrac{1}{2}$ × (Sum of parallel sides) × height

= $\dfrac{1}{2}$ × (AB + CD) × 12

= $\dfrac{1}{2}$ × 36 × 12

= 18 × 12

= 216 cm².

Hence, area of trapezium = 216 cm².