Area of Trapezium

In this page area of trapezium we are going to see the formula to find area of parallelogram 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 ) x 4

                                        =  (1/2) x (17) x 4

                                        =  17 x 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 the two parallel sides be "a" and "b"

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) x h  =  64

             (1/2) (a + a + 2) x 4 = 64

              (1/2) (2a + 2) x 4 = 64

                      2 (2a + 2) = 64

                          2a + 2 = 64/2

                          2a + 2 = 32 

                                2a = 32 - 2

                                 2a = 30

                                  a = 30/2

                                  a = 15 cm

                                  b = a + 2

                                  b = 15 + 2

                                  b = 17 cm

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


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Area of Trapezium to Formulas for Shapes