 A trapezium is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases and the other two sides are called the legs. To find the area of a trapezium, we need to know the lengths of the bases and the height. The height is the distance between the parallel bases and is perpendicular to them. Once we have these measurements, we can use the formula for the area of a trapezium to calculate the area.

## What is Area of a trapezium?

The area of a trapezium is the amount of space inside the shape. It is a measure of the size of the trapezium. The formula to calculate the area of a trapezium is:

Area = (a+b)h/2

where “a” and “b” are the lengths of the parallel sides (also called the bases) and “h” is the height (the distance between the parallel bases and is perpendicular to them).

For example, if the lengths of the bases are 10 and 15 units, and the height is 8 units, then the area of the trapezium would be:

Area = (10 + 15) * 8 / 2 = 125 square units.

It’s important to note that the height of trapezium must be perpendicular to the parallel sides.

### Area of Trapezium Formula :

The formula to calculate the area of a trapezium is as follows:

Area = (a + b)h/2

where:

• “a” and “b” are the lengths of the parallel sides (also called the bases)
• “h” is the height (the distance between the parallel bases and is perpendicular to them)

This formula is based on the fact that a trapezium can be divided into a rectangle and two triangles. The area of the rectangle is equal to the product of the height and the average of the two bases (a+b)/2, and the area of each triangle is equal to half of the product of the height and the distance between the two bases. Adding these areas together gives the total area of the trapezium.

Also Read : How to Divide Fractions

### How to Derive Area of Trapezium Formula?

The area of a trapezium can be derived by splitting the trapezium into a rectangle and two triangles and then adding their areas together. Here’s one way to derive the formula:

1. Draw a trapezium with parallel sides “a” and “b” and height “h”.
2. Draw a line segment, parallel to the bases, from the midpoint of the non-parallel side to the opposite parallel side.
3. Now the trapezium is split into a rectangle and two triangles. The rectangle has an area of (a+b)h/2, and each of the two triangles has an area of h(b-a)/2.
4. Adding the areas of the rectangle and the two triangles together gives the total area of the trapezium: (a+b)h/2 + h(b-a)/2 + h(b-a)/2 = (a+b)h/2
5. So the area of the trapezium is (a + b)h/2.

It’s important to note that the height of trapezium must be perpendicular to the parallel sides, otherwise the formula will not be correct.

## How to find the area of a trapezium

To find the area of a trapezium, you will need to know the lengths of the parallel sides (also called the bases) and the height. Once you have these measurements, you can use the formula for the area of a trapezium to calculate the area.

Here is an example of how to use the formula:

1. Measure the lengths of the parallel sides (bases) of the trapezium. Let’s say the lengths are 10 units and 15 units.
2. Measure the height of the trapezium. Let’s say the height is 8 units.
3. Use the formula to calculate the area of the trapezium: Area = (10 + 15) * 8 / 2 = 125 square units.

It’s important to note that the height of trapezium must be perpendicular to the parallel sides, otherwise the formula will not be correct.

### Properties of a Trapezium

• A trapezium is a quadrilateral with one pair of parallel sides, called the bases.
• The non-parallel sides are called the legs.
• The height of a trapezium is the distance between the parallel bases and is perpendicular to them.
• The area of a trapezium can be calculated using the formula: Area = (a + b)h/2, where “a” and “b” are the lengths of the parallel sides (bases) and “h” is the height.
• A trapezium can be further classified into different types, such as right trapezium, isosceles trapezium, and more, depending on the properties of the angles, side lengths and height.

Also Read : What is Axis of Symmetry

### Applications of Trapezium:

• Trapeziums can be used in construction and engineering, such as in the design of bridges, buildings, and other structures.
• Trapeziums are also used in geometry and trigonometry, to calculate area and other properties.
• Trapeziums are used in physics and engineering, to calculate the force and pressure distribution in structures like beams and trusses.
• Trapeziums are widely used in the field of surveying for the calculation of areas of plots of land, and other objects.
• Trapeziums are used in mechanics to calculate the force and pressure distribution in structures like beams and trusses.

Note that the above are just a few examples, and the usage of trapeziums can be even more varied in different fields like art, graphic design, computer science and more.

### Area of Trapezium Examples

Here are a few examples of how to find the area of a trapezium using the formula:

`A trapezium has parallel sides of length 8 units and 12 units, and a height of 6 units. `

The area of the trapezium is: Area = (8 + 12) * 6 / 2 = 54 square units.

`A trapezium has parallel sides of length 15 units and 20 units, and a height of 10 units. `

The area of the trapezium is: Area = (15 + 20) * 10 / 2 = 175 square units.

`A trapezium has parallel sides of length 6 units and 9 units, and a height of 7 units. `

The area of the trapezium is: Area = (6 + 9) * 7 / 2 = 39.5 square units.

`A trapezium has parallel sides of length 14 units and 18 units, and a height of 9 units. `

The area of the trapezium is: Area = (14 + 18) * 9 / 2 = 153 square units.

`A trapezium has parallel sides of length 5 units and 7 units, and a height of 9 units. `

The area of the trapezium is: Area = (5 + 7) * 9 / 2 = 36 square units.

`A trapezium has parallel sides of length 11 units and 13 units, and a height of 6 units. `

The area of the trapezium is: Area = (11 + 13) * 6 / 2 = 72 square units.

`A trapezium has parallel sides of length 8 units and 10 units, and a height of 4 units. `

The area of the trapezium is: Area = (8 + 10) * 4 / 2 = 32 square units.

`A trapezium has parallel sides of length 12 units and 16 units, and a height of 10 units. `

The area of the trapezium is: Area = (12 + 16) * 10 / 2 = 120 square units.

`A trapezium has parallel sides of length 14 units and 18 units, and a height of 8 units. `

The area of the trapezium is: Area = (14 + 18) * 8 / 2 = 104 square units.

Remember, to calculate the area of a trapezium, you need to know the lengths of the parallel sides (bases) and the height of the trapezium. With this information, you can use the formula to find the area of the trapezium. It’s important to note that the height of trapezium must be perpendicular to the parallel sides, otherwise the formula will not be correct.

## FAQ’s

#### 1.What is a trapezium?

A trapezium is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases and the other two sides are called the legs.

#### 2.What are the properties of a trapezium?

A trapezium is a quadrilateral with one pair of parallel sides, called the bases. The non-parallel sides are called the legs. The height of a trapezium is the distance between the parallel bases and is perpendicular to them. The area of a trapezium can be calculated using the formula: Area = (a + b)h/2, where “a” and “b” are the lengths of the parallel sides (bases) and “h” is the height.

#### 3.How can I find the area of a trapezium?

To find the area of a trapezium, you will need to know the lengths of the parallel sides (also called the bases) and the height. Once you have these measurements, you can use the formula for the area of a trapezium to calculate the area. The formula is as follows: Area = (a + b)h/2, where “a” and “b” are the lengths of the parallel sides (bases) and “h” is the height.

#### 4.Are there different types of trapeziums?

Yes, there are different types of trapeziums such as right trapezium, isosceles trapezium, and more, depending on the properties of the angles, side lengths, and height.

#### 5.What are some applications of trapeziums?

Trapeziums can be used in construction and engineering, such as in the design of bridges, buildings, and other structures. They are also used in geometry and trigonometry, to calculate area and other properties. Additionally, trapeziums are used in physics and engineering, to calculate the force and pressure distribution in structures like beams and trusses. They are also used in surveying, mechanics and other fields.

#### 6.Is it necessary that the height of trapezium be perpendicular to the parallel sides?

Yes, it is necessary that the height of the trapezium be perpendicular to the parallel sides for the formula to be correct. If the height is not perpendicular, the formula will not give the correct area of the trapezium.

## Conclusion:

In conclusion, finding the area of a trapezium is a simple process that involves measuring the lengths of the bases and the height, and then using the formula for the area of a trapezium. With this information, you will be able to calculate the area of a trapezium with ease. Remember that a trapezium is a quadrilateral with one pair of parallel sides, and the area of a trapezium is given by the formula: Area = (a+b)h/2, where “a” and “b” are the lengths of the parallel sides and “h” is the height.