How to find the Distance Between Parallel Sides of a Trapezium?

Solution:

Since the formula for the area of a trapezium uses the sum of parallel sides and the distance between them, it implies that if any of the two quantities is given, the third can be computed conveniently. Thus, if area and the sum of parallel sides of a trapezium is given, the distance between them can be calculated by substituting the given values in the formula for the area of a trapezium.

Example: Suppose a trapezium ABCD with an area of 350 cm² has parallel sides of the measures 25 cm and 10 cm respectively. Then, its height, i.e. the distance between its parallel sides can be calculated by substituting the given values in the formula for the area of a trapezium.

Solution:

Area = 1/2×[(sum of parallel sides)×(height of trapezium)]

Area = 1/2×(25 + 10)×H

350  = 1/2×35×H

H = 20 cm

A trapezium is a quadrilateral with one pair of parallel opposite sides, according to Euclidean geometry. A trapezium is derived from the Greek word “trapeza,” which means “table.” It is a two-dimensional quadrilateral (made up of four straight lines) with two parallel opposite sides. The opposite parallel sides are referred to as the trapezium’s base, while the non-parallel sides are referred to as its legs. It has four sides and four corners and is a closed plane shape. It is also called a trapezoid. 

Since a trapezium is a quadrilateral, it has 4 different sides and 4 different edges. The measures of all 4 internal angles of a trapezium always sum up to 360°.