Trapezoids are two-dimensional geometric figures enclosed by four sides having a pair of sides parallel to each other and another non-parallel. Want to learn all about trapezoids? In this article, we’ve discussed the basic concept and properties of trapezoids including their meaning, types, and formulas.
What is the Definition of a Trapezoid?
A trapezoid is a two-dimensional quadrilateral (having four sides) enclosed by two parallel sides. The other name for a trapezoid is a trapezium. The parallel sides of the trapezium are its bases and non-parallel sides are described as legs or lateral sides. The altitude of the trapezoid is the shortest distance between its two parallel sides.
What are the Different Types of Trapezoid?
There are three types of trapezoid:
- Right Trapezoids: The right trapezoids have a pair of right angles making them a right-angled trapezoid. A right trapezium is used when the area under the curve is to be estimated.
- Isosceles Trapezoids: When the non-parallel sides or legs of the trapezium are equal in length then the particular trapezium is known as an isosceles trapezoid. The angles of the base (parallel sides) of a trapezium are equal to each other.
- Scalene Trapezoids: When no sides or angles are equal to each other then the particular trapezium is known as a scalene trapezoid.
What is the Formula to Calculate the area and Perimeter of a Trapezoid?
1. Calculating Area of a Trapezoid:
When calculating the area of trapezoid, first, the average of the two parallel sides (bases) is computed and then it is multiplied by the altitude (height). The mathematical formula to calculate the area of trapezium is as follows:
Area = 1/2 (a+b) h
2. Calculating Perimeter of Trapezoid:
For calculating the perimeter of the trapezoid, the sum of all its sides is computed. Therefore, for a trapezium having sides A, B, C, and D, the mathematical formula to calculate the perimeter of the trapezium is as follows:
Perimeter = A + B + C + D
What are the Properties of a Trapezoid?
The below-given are some properties of trapezoids:
- A pair of sides known as bases are parallel to each other.
- The non-parallel opposite sides of isosceles trapezoids are of equal length.
- The diagonals and angles on parallel sides of an isosceles trapezium are equal.
- Angles next to each other in a trapezoid sum up to 180°
- If a median is drawn on a trapezium then it will be parallel to its bases and its length will be average to the length of parallel sides [(a + b) / 2].
- The intersection point of the diagonals in a trapezium is collinear to the midpoints of the two opposite sides.
- Consider a trapezium with sides a, b, c, and d and diagonals p and q. In such a case the following given equation will be true: p2+q2= c2+d2+2ab
- A trapezoid is called a parallelogram when the pairs of its opposite sides are parallel to each other.
- A trapezoid is called a square when all sides are equal, all angles are right-angled, and the pairs of opposite sides are parallel to each other.
- A trapezoid is called a rectangle when all angles are right-angled and pairs of opposite sides are parallel and equal in length.
Going through the above-given article will help you to learn every concept of trapezoids including the perimeter and area of a trapezoid. Cuemath is the world’s leading educational platform that offers after-school live classes for math and reasoning. If you have any doubts related to the above-described concept then you can learn all about trapezoids via this specific platform.