Trapezoid Area Formula

In geometry, we are having objects with various shapes and sizes. One such shape is a trapezoid. It is a little bit uncommon in comparison to other kinds of shapes. It comes under the categories of quadrilaterals, as it has four sides. A trapezoid is a two-dimensional geometric figure which has four sides and at least one set of opposite sides parallel. In this article, we will discuss the trapezoid area formula with examples. Let us learn this topic in easy terms!

Trapezoid Area Formula

Definition and Structure of Trapezoid

A Trapezoid is a specific type of quadrilateral, i.e. it has four sides. Out of those one pair of sides are parallel with unequal lengths. These two parallel sides are called the bases. While the other sides are called the legs. The other two sides are not parallel but may be equal or unequal lengths.

To make a trapezoid, we need a triangle. Any triangle will do the purpose i.e. right, obtuse, isosceles, and scalene. Then slice off the top of the triangle to make the cut parallel to the bottom of the triangle. Now we will have a small triangle and a trapezoid.

There are different types of trapezoids. Some of these are an isosceles trapezoid, right trapezoid, scalene trapezoid, etc. A trapezoid with the two non-parallel sides having the equal length is called an isosceles trapezoid. A right trapezoid is having at least two right angles. A right isosceles trapezoid is a trapezoid which is simultaneously a right trapezoid as well as an isosceles trapezoid.

Source: en.wikipedia.org

The formula for Area of a trapezoid:

The area can be computed with the help of the following simple steps to arrive at the trapezoid area formula,

• Step-1: Add the two parallel bases.
• Step-2: Multiply the result of the above step with the height of the trapezoid.
• Step-3: Divide the result of step-2 by 2.
• Step-4: We will get the area of the given trapezoid.

Mathematically formula is given as,

\(A = \frac {(a+b) \times h}{2}\)

A	Trapezoid area
h	Height (it is the perpendicular height, not the length of the legs.)
a	The short base
b	The long base

Solved Examples

Q.1: Find out the area of a trapezoid whose bases are 25 cm and 31 cm and the perpendicular height is 7 cm?

Solution: As given in the problem,

a = 25 cm; b = 31 cm; h = 7 cm

Now applying the formula for the area of a trapezoid,

\(A = \frac {(a+b) \times h}{2}\)

\(= \frac {(25+31) \times 7}{2}\)

\(= 196 \;square cm\)

Therefore the area of the trapezoid will be 196 square cm.

Q.2: A field is given in the trapezoidal shape. Its two parallel bases are of lengths 13 m and 20 m. If the area of the field is 2400 square m. Then find out the perpendicular distance between the two parallel bases.

Solution: As given,

a = 13 m; b = 20 m; A = 2400 square m

Now, formula for area of trapezoid is,

\(A = \frac {(a+b) \times h}{2}\)

Rearranging it,

\(h = \frac{2 \times A}{ (a+b)}\)

\(= \frac{2 \times 2400}{ (13 + 20)}\)

= 145.45 m

Perpendicular distance is 145.45 m.