What is a Trapezoid in Math? (Definition, Shape, Examples) - BYJUS

# Trapezoids

We know that a quadrilateral is a polygon with four sides and that there are various types of quadrilaterals such as a square, a rectangle, a trapezoid, a rhombus, and so on. Here we will learn about trapezoids, their properties and some related formulas....Read MoreRead Less

## What is a Trapezoid?

A trapezoid is a quadrilateral with exactly one pair of opposite sides that are parallel. The pair of opposite sides that are parallel are usually the top and the bottom sides of a trapezoid.

## Properties of a Trapezoid

• The parallel sides are called bases
• The non-parallel sides are called legs
• The perpendicular distance between the bases is called height or altitude
• The two consecutive angles with a common side as the base are called base angles
• The angles formed on the same leg, between the parallel sides, are supplementary
• The sum of all interior angles is 360°

## Area of a Trapezoid

The area A of trapezoid is one half of the product of its height h and sum of its bases b$$_1$$ and b$$_2$$.

A = $$\frac{1}{2}$$ x h x (b$$_1$$  + b$$_2$$ )

It must be noted that the area of geometric shapes is measured in square units.

## Types of Trapezoids

There are three types of trapezoids:

• Right trapezoid
• Isosceles trapezoid
• Scalene trapezoid

1. Right trapezoid : A trapezoid with one pair of adjacent right angles is called a right trapezoid.

2. Isosceles trapezoid : A trapezoid whose non parallel sides, called legs, are congruent or equal in length is called an isosceles trapezoid. The base angles of an isosceles trapezoid are equal.

3. Scalene trapezoid : A trapezoid that has no sides that are equal in length is a scalene trapezoid.

## Solved Trapezoid Examples

Example 1:  Find the area of the given trapezoid.

Solution:

A = $$\frac{1}{2}$$ x h x (b$$_1$$ + b$$_2$$)           [Write the formula]

A = $$\frac{1}{2}$$ x 4 x (5 + 6)              [Substitute]

A = 22

So, the area of the given trapezoid is 22 square inches.

Example 2: A garden is in the shape of a trapezoid as shown in the image. The area of the garden is 10000 square meters. Find the shortest distance between the parallel sides of the garden?

Solution: The shortest distance between the parallel sides is the height of the trapezoid.

We can use the formula for the area of a trapezoid to find the height.

A = $$\frac{1}{2}$$ x h x (b$$_1$$ + b$$_2$$)                         [Write the formula]

10000 = $$\frac{1}{2}$$ x h x (150 + 100)             [Substitute 10000 for A, 150 for b$$_1$$ and 100 for b$$_2$$]

10000 x 2 = h x 250                        [Multiply by 2 on each side.]

$$\frac{20000}{250}$$ = h                                          [Divide each side by 250]

80 = h                                              [Solve]

So, the shortest distance between parallel sides of the trapezoid shaped garden is 80 meters.

Example 3: Find the value of x.

Solution :

The given trapezoid shows that AD = BC, so this is an isosceles trapezoid.

∠ADC = ∠BCD                     [Base angles of an isosceles trapezoid are equal]

65 = x + 15                           [Substitute 65 for ∠ADC and x + 15 for ∠BCD.]

65 – 15 = x + 15 – 15            [Subtract 15 on both sides]

50 = x                                  [Solve]

So, the value of x is 50.