How to Derive Area of Trapezium Formula?
The formula for the area of a trapezium can be obtained in two different ways,
- By using a parallelogram
- By using a triangle
Derivation of Area of Trapezium Formula Using a Parallelogram
In order to find the area of a trapezium formula using a parallelogram, take two trapeziums that are the same (equal sides and angles), their parallel sides are a and b, and the height of the trapezium is h. Place the second trapezium upside down. It is clear that in this way if both the trapeziums are joined, it will become a parallelogram.
Now, after joining both trapeziums, the trapeziums will form one parallelogram,
Let’s say that the area of one trapezium is A, and the area of a parallelogram will be twice the area of the trapezium, that is, 2A. The area of a parallelogram is base × height. Therefore,
2A = Base × Height
Base = (a + b)
Height = h
2A = (a + b) × h
A = 1/2 × (a + b) × h
Derivation of Area of Trapezium Formula Using a Parallelogram
Consider a trapezium with parallel sides as a and b and height as h. In order to find the area of the trapezium formula using a triangle, bisect the non-parallel side of the triangle, join it from the corner to make a small triangle, flip the triangle and make it into a bigger triangle (As shown below).
It is observed that the area of the bigger triangle and the area of the original trapezium are equal. The base of the triangle is (a + b). The area of the triangle is given as,
A = 1/2 × base × height
A = 1/2 × (a + b) × h = Area of Trapezium
What is the formula to find the area of a Trapezium?
Area of a trapezium is the number of unit squares that can fit into the trapezium, and it is measured in square units. The trapezium, which is also known as the trapezoid, is a closed quadrilateral that contains a pair of parallel sides, whereas the other pair of sides are not parallel. The sides may or may not vary in length.
The parallel sides of the trapezium are called the bases of the trapezium. The distance between the bases is known as the height of the trapezium. The height of the trapezium is also known as the altitude. The non-parallel sides of the trapezium are known as the legs. The sum of the interior angles of the trapezium is 360°. It has 4 sides and 4 vertices.