The distance between parallel sides of a trapezium is 15 cm and the length of the line segment joining the mid-points of its non-parallel sides is 26 cm. Find the area of the trapezium.

Given:

Let the given trapezium be as shown in the figure below:

The distance between parallel sides of a trapezium, (i.e., height) = 15 cm

The length of the line segment joining the mid-points of its non-parallel sides, EF = 26 cm

Since EF is half of the sum of the lengths of the parallel sides.

EF = $\dfrac{1}{2}$ x (AD + BC)

⇒ $\dfrac{1}{2}$ x (AD + BC) = 26

⇒ AD + BC = 26 x 2 cm = 52 cm

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

= $\dfrac{1}{2}$ x (AD + BC) x height

= $\dfrac{1}{2}$ x 52 x 15

= 26 x 15

= 390 cm²

Hence, the area of the trapezium is 390 cm².