# Trapezoids

Trapezoid Shapes Maths

While learning two-dimensional shapes, we will come across the shape trapezium or trapezoid. So let’s learn what a trapezoid is.

A four-sided 2-dimensional figure with one of its opposite sides parallel and the other two sides non-parallel is said to be a trapezoid. The opposite sides are called the bases, the nonparallel sides are called the leg of the trapezoid, and the perpendicular distance between the two parallel sides is the altitude or height of the trapezoid.

Trapezoids Definition

A quadrilateral with one of its sides parallel and the other two sides are non-parallel is called a trapezoid. A trapezoid is also known as trapezium.

Trapezoid Shapes

After understanding the concept of what a trapezoid is, now let us see trapezoid shapes. Trapezoid shapes maths will help you to identify different trapezoid shapes. According to the trapezoid definition, a trapezoid is a four-sided figure with two parallel sides and two non-parallel sides. There are different trapezoid shapes or you can say according to their shapes, trapezoids are of different types.

Different Trapezoid Shapes Maths

Let us first see the different properties of a trapezoid and different types of trapezoids. Properties of a trapezoid will be helpful to you to construct a trapezoid.

Properties of a Trapezoid

Some of the basic properties of a trapezoid are as follows,

• Bases are parallel to each other.
• Lower base angle and upper base angle form a linear pair i.e 1800.
• The median is parallel to both the bases. And median’s length is the average of the two base lengths, i.e.m = a+b/2
• In a trapezoid, if both pairs of its opposite sides are parallel it will be a parallelogram.
• In a trapezoid, if both pairs of its opposite sides are parallel and all its sides are of equal length and at right angles to each other then it is a square
• In a  trapezoid, if both pairs of its opposite sides are parallel; its opposite sides are of equal length and are at right angles to each other then it is a rectangle.

Types of Trapezoids:

Different types of trapezoids are:

• Right Trapezoids
• Isosceles Trapezoids
• Scalene Trapezoids

Right Trapezoids

A trapezoid that has a pair of right angles is said to be a right trapezoid.

Isosceles Trapezoids

In a given trapezoid if the non-parallel sides or the legs of a trapezoid are equal in length, it is known as an Isosceles trapezoid.

Scalene Trapezoids

In a given trapezoid, if neither the sides nor the angles of a trapezium are equal, we call it a Scalene trapezoid.

Area of Trapezoid

The area of the trapezoid is calculated by multiplying the mean of the bases by the height of the trapezoid.

Area of Trapezoid = ( a + b/2 ) x h, where a and b are two bases and h is the height of the trapezoid.

 Area of Trapezoid = ½ ( a+ b) h

Perimeter of Trapezoid

The perimeter of a trapezoid is the sum of all sides. If a, b, c, and d  are all the four sides of a trapezium then perimeter formula is given by-

Perimeter of trapezoid = a + b + c + d

 Perimeter of trapezoid = a + b + c + d

Median of a Trapezoid

The median is a line segment drawn from the midpoints of the non-parallel side such that it is parallel to both the bases.

The median’s length is calculated as the average of the two base lengths:

m = a+b/2, where a and b area base lengths

If the median is given we can even calculate the area of the trapezoid by the formula

A = m x h

 Median of a trapezoid  = a+ b /2

Oblique Side of a Right Trapezoid

Here B and b are the base of the Right Trapezoid, h is the height and l is the oblique side of a trapezoid.

n = B – b

$I=\sqrt{h^2+n^2}$

Isosceles Trapezoid Height

Here B,b is the base, h is the height, and l is the oblique side.

n = B – b/2

$h=\sqrt{l^2-n^2}$

Solved Examples

Example 1: Given a trapezoid with bases of 6 meters and 10 meters and a height of 5 meters.find the area of the trapezoid.

Solution: we have a = 6cm, b = 10m and h = 5m

By Area of trapezoid = ½ ( a + b) h

= ½ ( 6 + 10) x 5

= ½ ( 16) x 5

= 8 x 5

= 40m2

Example 2: If the trapezoid has the bases as 5cm, 8cm and 4cm and 6cm. Find the perimeter of the trapezoid.

Solution: We have a = 5cm, b = 8cm, c = 4cm, and d  = 6cm then

By perimeter formula we have

Perimeter of trapezoid = a + b + c+ d

= 5 + 8 + 4 + 6

= 23 cm

Quiz Time

1. The perimeter of an isosceles trapezoid is 120 m and the bases are 50 and 30 m. Calculate the area of the trapezoid and the length of the non-parallel sides.

2. Find the area of a trapezoid if its bases are given as 12cm and 4 sm respectively. And the height of the trapezoid is 7cm.