Trapezoid Formulas

Formulas for trapezoid consists of Area of Trapezoid and Perimeter of Trapezoid, let’s learn the same in detail.

Area of Trapezoid

Let us consider a trapezoid  PQRS, SR and PQ are parallel sides and ST is the shortest distance between them which is perpendicular and is denoted with h.

Let‘s divide the trapezoid into segments. That gives us two triangles PTS and UQR and a rectangle TURS. Now if we find the areas of all three and sum them, we get the area of the Trapezoid.

Area of triangle, PTS = 1/2 (base × height) 

Area of triangle, PTS = 1/2 (PT × ST)

= 1/2 (xh)……(1)

On writing the area of rectangle TURS = length × breadth  

Area of rectangle TURS = bh……(2)

In writing the area of triangle UQR = 1/2 (base × height) 

Area of triangle UQR = 1/2 ( yh)…..(3)

In summing up the three areas i.e. equations (1), (2), and (3), we get the area of the trapezium.

On adding all the three equations, 

Area of Trapezoid = 1/2 (xh) + bh + 1/2 ( yh)

on taking 1/2 (h) common, we can write the equation as 

Area of Trapezoid = (1/2) h (x + 2b + y)

Area of Trapezoid = (1/2) h ( x + b + b + y)

From the figure, we can observe that summing x, b, and y gives a. So,

Area of Trapezoid = (1/2) × h × (a+b)

or

Area of Trapezoid = (1/2) × (height) × (sum of the parallel sides)

Perimeter of Trapezoid

For finding the perimeter, the lengths of all the sides are to be added. 

Perimeter of Trapezoid = Sum of lengths of parallel and non-parallel sides

For any trapezoid ABCD with sides, AB = a, BC = b, CD = c, DA = a, its perimeter is:

Perimeter of Trapezoid = a + b + c + d

Hence, the Perimeter of a trapezoid is the sum of lengths of parallel sides and the sum of lengths of non-parallel sides. 

Read More,

• Rhombus
• Triangle
• Quadrilaterals

Trapezoid is another name of trapezium and is a quadrilateral in which one pair of opposite sides are parallel. It is a quadrilateral and follows all the properties of a quadrilateral.

In this article we have covered, Trapezoid definition, types of trapezoid, properties of trapezoid, formulas of trapezoid and related example in detail.