A Remarkably Easy Way to Calculate the Area of a Trapezoid

Omkar Phatak Apr 23, 2019
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If you need to know the formula and technique for calculating trapezoid area, then you have landed on the right page. You will find what you are looking for, in the following write-up.
A trapezoid (also known as 'trapezium' in British English) is a quadrilateral, that has one pair of parallel sides. Some mathematicians also define it as a quadrilateral that has at least one pair of parallel sides. This second alternative definition, makes parallelograms, rhombuses, squares, and rectangles to be special cases of trapezoids.
The parallel sides may be unequal in length and the rest of the two sides may not be parallel. If the two non-parallel sides are equal in length, it is called an isosceles trapezoid. The base angles of such a figure are equal.

Properties

For any quadrilateral to be called a trapezoid, is that it must have two adjacent angles, whose sum is 180°. That means, every trapezoid has to have a pair of supplementary angles. Another interesting property is that a line drawn, joining the mid-points of the parallel sides of every trapezoid, divides it into two parts with equal areas.

Calculation

There are two main formulas that can serve the purpose of calculating trapezoid area. One uses the height as a parameter, along with the lengths of parallel sides, while the other one gives the area by using just the lengths of sides as parameters.

Area Formula (With Height)

Let us see what the area formula is, when the height is known.

Area = ½ x Height x (Sum of Lengths of Parallel Sides) = ½ H (a + b)

where 'H' is the height of the trapezoid, while 'a' and 'b' are the lengths of its parallel sides. The unit of area will be cm2 or m2.

Area Formula (Without Height)

What if the height is not known or provided in the problem? What do you do then? In such a case, there is another formula:

Area = [(a + b) / (b - a)] x √[(s - b) (s - a) (s - b - c) (s - b - d)]
where 'a' and 'b' are the lengths of the parallel sides, 'c' and 'd' are the lengths of the other two sides and 's' is the semi-perimeter of the trapezoid given by (s = (a + b + c + d) / 2).
Calculating area of any geometrical object is just a matter of plugging in numbers. Find out the derivation of the formulas stated earlier and derive the area equation once. It will acquaint you with the method of geometric derivations and besides that, it will be a good exercise for your brain.