Area of Trapezium

Trapezium is a 2-dimensional geometric shape with 4 sides and 4 vertexes. It is a quadrilateral and has 4 sides out of which 2 sides are parallel to each other.

Some of the properties of a trapezium are listed below:

  1. The sum of the angles of a trapezium is 360º
  2. A trapezium is not a parallelogram (as only one pair of opposite sides is parallel in a trapezium and we require both pairs to be parallel in a parallelogram).
  3. The 4 sides of a trapezium are unequal unless it is an isosceles trapezium in which the 2 parallel sides are equal.
  4. The diagonals of a trapezium bisect each other.
  5. Two pairs of adjacent angles of a trapezium sum up to 180 degrees.

Area of Trapezium

The area of a trapezium is equal to the sum of the areas  of the two triangles and the area  of the rectangle.

the area of a trapezium is given by the formula:

Area of Trapezium = 1/2 x distance between the parallel sides x Sum of parallel sides

Area = 1/2 x h x (AB + DC)


Q1. Two parallel sides of a trapezium are of lengths 27 cm and 19 cm respectively, and the distance between them is 14 cm. Find the area of the trapezium.


Area of the trapezium = ¹/₂ × (sum of parallel sides) × (distance between them)

Area of the trapezium = {¹/₂ × (27 + 19) × 14} cm² = 322 cm²

Q2. The area of a trapezium is 352 cm² and the distance between its parallel sides is 16 cm. If one of the parallel sides is of length 25 cm, find the length of the other.


Let the length of the required side be x cm.

Then, area of the trapezium = {¹/₂ × (25 + x) × 16} cm²

Area of the trapezium = (200 + 8x) cm².

But, the area of the trapezium = 352 cm² (given)

Therefore, 200 + 8x = 352

                ⇒ 8x = (352 – 200)

⇒ 8x = 152

⇒ x = (152/8)

⇒ x = 19.

The length of the other side is 19 cm.

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