Area of Trapezium

A trapezium is a convex quadrilateral. It is a 2-dimensional shape. It contains one pair of opposite sides parallel to each other. To find the area of the trapezium, we need the sum of parallel sides and the distance between the parallel sides.

Euclidean Geometry defines the quadrilateral as a polygon with four sides and four vertices.

Trapezium

The trapezium has one pair of parallel sides. A parallelogram is a special case of it.

Trapezium (Source)

Types of Trapezium   

The are three types of Trapezium:

  1. Isosceles Trapezium
  2. Scalene Trapezium
  3. Right Trapezium

Isosceles Trapezium

Isosceles Trapezium

The non-parallel sides or legs are equal to each other.

Scalene Trapezium

All of the angles are different from each other in the Scalene trapezium.

Scalene trapezium

Right trapezium

Two adjacent angles are right angles.

Right trapezium

Properties of a Trapezium

  1. One pair of sides are parallel to the other.
  2. Diagonals intersect each other.
  3. The line joining mid-point of non-parallel sides is always parallel to the parallel sides.

Formulas of a Trapezium

Area = \(\frac{1}{2} \cdot \text{Sum of Parallel Sides} \cdot \text{Distance between parallel sides}. = \frac{1}{2} \cdot (a + b) \cdot h\)

Perimeter = Sum of all four sides.

= a + b + c + d

Area of isosceles trapezium = \(\frac{1}{2} \cdot (a + b) \cdot (\sqrt{d^2 – (a-c)^2}\)

Isosceles Trapezium

The perimeter of Isosceles Trapezium = Sum of all four sides.

= a + 2b + c

Application

Trapezoidal rule – Estimating area under the curve by dividing the area under the curve into a number of trapeziums and finding the area of each trapezium.

Read more: Trapezium Rule

Questions

  1. Find the Trapezium area with the sum of parallel sides of 40cm and a height of 20cm.

Area of Trapezium = [Latex]\frac{1}{2} \cdot \text{Sum of Parallel Sides} \cdot \text{Distance between parallel sides}[\Latex]

= \(\frac{1}{2} \cdot 40 \cdot 20\)

= \(400cm^2\)

  1. Find the perimeter of the Trapezium with sides 4cm, 8cm, 3cm, and 2cm.

The perimeter of trapezium = Sum of all the sides of a trapezium

= 4 + 8 + 3 + 2

= 17cm.

What is a Trapezium?

A trapezium is a convex quadrilateral. The trapezium is a 2-dimensional shape. It contains one pair of opposite sides parallel to each other.  

Can a square be a trapezium?

Square is a particular case of a trapezium with all sides being the same and all angles being \(90$^\circ$\).

What is isosceles trapezium?

In isosceles trapezium the non parallel sides area equal.

What is the formula for the area of the trapezium?

Area of Trapezium = \(\)\frac{1}{2} \cdot \text{Sum of Parallel Sides} \cdot \text{Distance between parallel sides}/latex]

Related Articles:
1. Area of Rhombus
2. Area of Quadrilateral
3. Area of Octagon
4. Area of Pentagon

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