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Mensuration is a discipline of mathematics that studies geometric shapes, their area, volume, and other associated properties. A trapezium is a kind of quadrilateral in which two of its sides are parallel and two are non-parallel. The two parallel sides of a trapezium are known as base. And (h) is considered to be the height/ altitude of the trapezium or the distance between two parallel sides. If the non-parallel side of a trapezium is equal then it will be an isosceles trapezium.

Table of content

  1. Formula of trapezium
  2. Area of trapezium formula proof
  3. Properties of trapezium
  4. Some questions based on trapezium
  5. Some practice questions based on the trapezium
  6. Conclusion
  7. FAQs

Formula of trapezium

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

Area of trapezium formula proof

Let ABCD be a trapezium of height h and AB||DC 

Join AC and draw perpendicular CL on AB and produce DC and draw perpendicular AM on DC.

Let CL and AM = h 

Area of trapezium = area of ∆ABC x area of ∆ACD

∴ Area of trapezium = 1/2 x sum of parallel sidesx( distance between them)

Properties of trapezium

  1. Trapezium is a closed figure in which sum of interior angles is equals to 360°
  2. It has a pair of the parallel side that are opposite to each other and both of them are known as base.
  3. The other two sides of a trapezium should be non-parallel and if these non-parallel sides of a trapezium are equal to each other then, the trapezium is said to be an isosceles trapezium.
  4. In trapezium sum of adjacent angles is equals to 180°
  5. At their intersection, the trapezoid’s diagonals cut each other in half.

Some questions based on trapezium

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

Solution –area of trapezium = ½ x (sum of parallel side) x (distance between them)

= 322 cm²

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

Solution – Given, the area of trapezium is 352 cm2. 

Distance between its parallel side = 16cm 

One side is 25 cm 

Let the other side be x 

Then by using formula –

325 = (200 + 8x) cm². 

8x = (352 – 200) 

 8x = 152 

x = (152/8) 

 x = 19. 

Some practice questions based on the trapezium

Q1. Find the area of a trapezium whose parallel sides are 24 cm and 20 cm and the distance between them is 15 cm. 

Q2. Find the area of a trapezium whose parallel sides are 38.7 cm and 22.3 cm, and the distance between them is 16 cm. 

Q3. The area of a trapezium is 1080 cm². If the lengths of its parallel sides are 55 cm and 34.4 cm, find the distance between them. 

Q4. The area of a trapezium is 1586 cm² and the distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm, find the other. 

Q5. The area of a trapezium is 405cm². Its parallel sides are in the ratio

4 : 5 and the perpendicular distance between them is 18 cm. Find the length of each of the parallel sides.

Conclusion

Mensuration is a discipline of mathematics that studies geometric shapes, their area, volume, and other associated properties. A trapezium is a quadrilateral in which two of its sides are parallel and two are non-parallel. (h) is considered to be the height/ altitude of the trapezium or the distance between two parallel sides. It has a pair of parallel side that are opposite to each other and both of them are known as based. If the non-parallel side of a trapezium is equal then it will be an isosceles trapezium.

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