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:
- The sum of the angles of a trapezium is 360º
- 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).
- The 4 sides of a trapezium are unequal unless it is an isosceles trapezium in which the 2 parallel sides are equal.
- The diagonals of a trapezium bisect each other.
- 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.