AREA OF TRAPEZIUM

About "Area of trapezium"

Area of trapezium :

Here we are going to see the formula to find area of trapezium and also we are going to see example problems to understand this topic.

Definition of trapezium :

The definition of trapezium is entirely different in both US and UK.

• In US a quadrilateral which is having no parallel sides is called trapezium.
• But in UK a quadrilateral which is having one pair of parallel sides is called trapezium.

Definition of trapezoid :

• In UK a quadrilateral which is having no parallel sides is called trapezoid.
• But in US a quadrilateral which is having one pair of parallel sides is called trapezoid.

Formula to find area of trapezoid :

Area = (1/2) (a + b) x h

Now we are going to see some examples to understand this topic.

Example 1 :

Find the area of the trapezium ABCD given in the below figure.

Solution :

Area of trapezium = (1/2) (a + b) x h

a = 5 cm , b = 12 cm and h = 4 cm

=  (1/2) (5 + 12) ⋅ 4

=   (1/2) ⋅ (17) ⋅ 4

=  17 ⋅ 2 

=  34 cm²

Example 2 :

In a trapezium the measurement of one parallel side two more than the other parallel side and the height is 4 cm. The area of the trapezium is 64 cm². Find the two parallel sides.

Solution :

Area of the trapezium = 64 cm²

Let  "a" and "b" are two parallel sides

One parallel side is two more than the other parallel side. So we can assume b as a + 2

Area of a trapezium = (1/2) (a + b) x h

(1/2) (a + b) ⋅ h  =  64

(1/2) (a + a + 2) ⋅ 4 = 64

(1/2) (2a + 2) ⋅ 4 = 64

2 (2a + 2) = 64 ==>  2a + 2 = 32 

2a = 30 ==> a = 15 cm

b = a + 2 ==> b = 15 + 2 ==> b = 17 cm

Therefore the two parallel sides are 15 cm and 17 cm.

Example 3 :

The shape of the top surface of a table is a trapezium. Find its area parallel if its parallel sides are 1 m and 1.2 m and perpendicular distance between 0.8 m

Solution :

Area of a trapezium = (1/2) (a + b) ⋅ h

=  (1/2) (1.2 + 1) ⋅ 0.8 

=  (1/2) (2.2) ⋅ 0.8 

=  1.1 (0.8)

=  8.8 m²

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