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)

Example

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.

Solution:

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.

Solution: 

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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