Definition of a Trapezoid

A trapezoid, or trapezium in some countries, is a four-sided quadrilateral shape with at least one pair of sides parallel to each other. Those sides parallel to each other are called bases and the others are legs.

Area of a Trapezoid

As we know a trapezium has a four-sided figure with at least one pair of parallel sides. It has an area formula to determine its area. In any case, you would first need to determine the length of the two bases-let's say, the first base and the second base. You have also to determine the height; that is the perpendicular distance between these two bases.

The formula of  area (A) of a trapezoid is given as,

Where,  

•   are the lengths of two bases.

• ℎ  is the height of the trapezoid.

Solved Problems on Area of Trapezoid

Problem1:

Find the area of the trapezoid if the bases of the trapezoid are 6 cm and 7 cm and the perpendicular distance between them is 8 cm.

Solution:

Given:

Let the parallel sides of a trapezium be  "a" and  "b" .

Therefore ,  a = 6 cm and b = 7 cm.

Also, given that the perpendicular distance between the parallel sides is 8 cm.

(i.e) h = 8 cm.

We know that the area of trapezoid formula is:

A = (½) [(a+b)h] square units

Using the given values in the formula, we get

                      A = (½) [(6+7)8] square units 

                      A = (6+7)4 cm2  

                      A = (13)4 cm2 

                      A = 52 cm2

Thus, the area of the trapezoid is 52 cm2.

Problem 2:

In the trapezoid, find the height of the trapezoid if the sum of the parallel sides is 25 m and the area is 75 .

Solution:

Given: a+b = 25 m

           Area, A = 75 .

 We need to find: h

The formula for area of trapezoid, 

           A = (½) [(a+b)h] square units

Putting the value in the formula, we get

                 75 = (½)[25h]

            75/25 = (½)h

                   3 = h/2

                   h = 6 .

 So, the height of the trapezoid is 6 m.

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