 # Trapezoid & Properties of Trapezoid

A trapezium is defined as a two-dimensional geometrical shape made up of one pair of parallel sides. We may witness different real-life instances of trapezium shapes, such as containers, luggage, popcorn boxes, and so on. The term ‘trapezium’ derives from the Greek word ‘trapeza,’ which means “table.” This 2-dimensional geometrical shape is categorized to be a quadrilateral, with the opposing parallel sides which are known as the trapezium’s bases as well as the remaining two sides known as the trapezium’s legs.

In this article, we are going to discuss the formula of the area of trapezium, properties of trapezium, several forms of trapeziums, and even some of the significant aspects of the quadrilateral.

## What is the Area of Trapezium?

We’ll go through a few steps to calculate the area of any given trapezium –

1. The first step we need to do is to note down any given dimensions of a trapezium. You need down the length of the sides of the trapezium which are parallel and also the length of the height if the trapezium.
2. You need to add all the lengths of the parallel sides of the trapezium.
3. Now, the third step is to find the product of the total of parallel sides & given height of trapezium.
4. The last step is to find the area of trapezium – You need to multiply 0.5 with the answer you obtained in step 3.

## Properties of Trapezium

Every geometrical figure in mathematics as it’s own set of properties. Let’s list down some properties of trapezium

• A trapezium is known to be a 2-dimensional figure.
• There are two diagonals in a trapezium & both of these diagonals are equal in length.
• The two diagonals in a trapezium always tend to intersect each other.
• Like every geometrical figure, a trapezium also has angles. And all the angles of the trapezium sum up to 360 degrees.
• There are two bases both of them are parallel.

## Formula to Calculate Area of Trapezium

The overall or total area occupied by a trapezium is referred to as the area of the trapezium. The area of a trapezium is very simple to calculate. We may easily determine it by taking the average of the trapezium’s two bases and multiplying it by its altitude as discussed above. To explain it mathematically, the area of a trapezium is: Area of trapezium formula is equal to height (h)* (a+b) / 2 square units, where the variables a and b are the trapezium’s bases and h is the altitude or height of the trapezium.

Area = h (a+b) / 2

## Solved Examples

Example 1: The height of a trapezium is equal to 8 units and the base of the trapezium is equal to 12 units & 14 units. How do you find the area of the given trapezium?

Solution: Let’s note down the information given in the question,

Height of Trapezium = 8 units

Base of Trapezium = 12 units & 14 units

Formula to find the area of Trapezium = height* (a+b) / 2

Area = 8*(12+14)/2 = 208/2 = 104 units.

Example 2: The height of a trapzeium is equal to 12 units and the base of trapezium is equal to 10 units & 14 units. How do you find the area of the given trapezium?

Solution: Let’s note down the information given in the question,

Height of Trapezium = 12 units

Base of Trapezium = 10 units & 14 units

Formula to find the area of Trapezium = height* (a+b) / 2

Area = 12*(10+14)/2 = 288/2 = 144 units.

Visit the Cuemath website, if you want to know more about the topic and solve more examples on trapeziums as well as area of trapzeium.