1. TRAPEZIUM

2. Let the distance between the two parallel sides be ‘h’.
A trapezium is a quadrilateral in which one pair of opposite sides is parallel.
The distance between the parallel sides is the height of the trapezium.
ABCD is a trapezium
Let the distance between the two parallel sides be ‘h’.
The diagonal BD
with parallel sides AB
and DC measuring ‘a’ and ‘b’.
divides the Trapezium into two triangles △ABD
and △BCD. D C B A b h a

3. Area of Trapezium = Area of △ABD + Area of △BCDh b a
Note:- If the non - parallel sides of a trapezium are equal (AD = BC), then it is
known as an isosceles trapezium.

4. sides are 4 cm and 8 cm of length. SOLUTION
EXAMPLE 1 : Find the area of the trapezium whose height is 12 cm and the parallel
sides are 4 cm and 8 cm of length.
SOLUTION
Given: h =12 cm , a = 4 cm , b = 8 cm
To find: Area of trapezium (A) 6
Divide 12 and 2 by 2
A = 6 x 12 = 72 cm2 (Ans)

5. To find: Height of trapezium (h)
EXAMPLE 2 : The length of the two parallel sides of a trapezium is 7 cm and 4 cm.
If its Area is 44 sq. cm. Find the distance between the parallel sides.
SOLUTION
Given: A =44 cm2 , a = 7 cm , b = 4 cm
To find: Height of trapezium (h) 4
Divide 44 and 11 by 11
h = 4x 2 = 8 cm (Ans)

6. Parallel side is 9 cm. Find the length of the other side SOLUTION
EXAMPLE 3 : The area of a trapezium is 84 sq. cm and its height is 14 cm. If one of its
Parallel side is 9 cm. Find the length of the other side
SOLUTION
Given: A =84 cm2 , h= 14cm , a = 9 cm
To find: one parallel side of trapezium (b) 7
Divide 14 and 2 by 2
= 7 x ( 9 + b) 12
Divide 84 and 7 by 7
9 + b = 12
b = = 3 (Ans)

7. Try these
Find the area of the trapezium whose height is 7 cm and the parallel sides are 3 cm and 5 cm of length.
The length of the two parallel sides of a trapezium is 4 cm and 5 cm. If its Area is 36 sq. cm. Find the distance between the parallel sides.