Trapezoid formula

In Geometry, a trapezium is one of the types of a quadrilateral with one pair of parallel sides (called bases) and one pair of non-parallel sides (called legs). The area of a trapezoid is the number of unit squares that can be fit into the trapezoid. It is generally measured using square units, such as cm², m², and so on. In this article, we are going to learn the area of trapezoid formula and examples in detail.

Area of Trapezoid Formula

To find the area of trapezoid, it is enough to know the bases (parallel sides) of trapezoid and the perpendicular distance between them.

If “a” and “b” are the parallel sides of trapezoid and “h” is the perpendicular distance between, then the area of trapezoid formula is given by:

Area of Trapezoid = (½) [(a+b)h] square units.

Examples on Area of Trapezoid

Example 1: 

Find the area of 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”.

Hence, 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

Now, substitute the 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

Therefore, the area of trapezoid is 52 cm².

Example 2:

Find the height of the trapezoid, if the sum of the parallel sides is 25 m and the area is 75 m².

Solution:

Given: a+b = 25 m

Area, A = 75 m².

To find: h

We know that the formula for area of trapezoid, A = (½) [(a+b)h] square units

Substituting the values in the formula, we get

75 = (½)[25h]

75/25 = (½)h

3 = h/2

h = 6.

Therefore, the height of the trapezoid is 6 m.

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