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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

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.

- 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°

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.

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.

**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.

Frequently Asked Questions

A parallelogram has both pairs of opposite sides parallel but a trapezoid has exactly one pair of opposite sides that are parallel. So, trapezoids are not parallelograms.

A trapezoid with legs that are equal in length is called an isosceles trapezoid.

When the legs of a trapezoid are parallel to each other, which indicates that both pairs of opposite sides are parallel, the trapezoid then becomes a parallelogram.

A quadrilateral with exactly one pair of opposite sides parallel is called a trapezoid.

The area of a trapezoid is one half of the product of its height and the sum of the length of its bases.