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Perimeter of a Trapezoid Formula

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Last updated date: 20th Apr 2024
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Perimeter of a Trapezoid Formula - Trapezoid Area Formula

A trapezium is a quadrilateral in which exactly one pair of opposite sides are parallel. Consider the following trapezium whose height and side lengths are known.


(Image will be Updated soon)


The perimeter of the trapezium is simply the sum of the lengths of its sides.

perimeter=AB+BC+CD+DA


To find the area of the trapezium, we break it into a parallelogram and a triangle, as shown in the diagram.

Area(trapeziumABCD) = Area(triangleADE) + Area(parallelogramABCE) =½ × (DE×h) + (EC×h)


Since opposite sides of a parallelogram are equal, EC=AB=b1

DE= DC−EC = b2−b1

⇒Area (trapeziumABCD)= h/2 ×(DE+2EC) = h/2 × (b2−b1+2b1)= h/2 × (b1+b2)


Let’s look at an Example to see How to use These Formulas.

  1. Calculate the perimeter and the area of a trapezium of height 5 cm if its parallel sides are 4 cm and 10 cm and its non-parallel sides are 6 cm and 8 cm.

Solution: Perimeter=4+10+6+8 = 28cm


Area=h/2 × (b1+b2)=5/2 × (4+10) = 35cm2


Why don’t you try solving the following problem now?


  1. A trapezium has an area of 20cm2. If its height is 4 cm and its non-parallel sides are 6 cm and 5 cm, then evaluate its perimeter.

Options:

(a) 21cm 

(b) 25cm 

(c) 27cm 

(d) none of these

Answer: (a)


Area=h/2 × (b1+b2) ⇒ 20 = 42 × (b1+b2) ⇒ b1+b2 = 10cm


Perimeter= 6+5+b1+b2 = 11+10 = 21cm

FAQs on Perimeter of a Trapezoid Formula

1. Is the trapezoid/trapezium considered a quadrilateral?

A quadrilateral is a closed shape with four sides, as we all know. As a result, a trapezoid/trapezium is sometimes called a quadrilateral. Some people describe a trapezoid as a quadrilateral with just one set of parallel sides (the exclusive definition), eliminating parallelograms from the definition. Others define a trapezoid as a quadrilateral having at least one pair of parallel sides (inclusive definition), which makes the parallelogram a specific sort of trapezoid. Angles of different dimensions can be found on a trapezoid.

2. Is there a difference between a trapezoid and a trapezium?

A trapezium is a quadrilateral with one set of opposing parallel sides. A trapezium's parallel sides are known as bases, and its non-parallel sides are known as legs. It's also known as a trapezoid. A trapezoid with two parallel sides is another name for a parallelogram.


A trapezium is a four-sided flat form with straight sides and opposing sides that are parallel. In the United States, it's known as a trapezoid.


A trapezoid is a quadrilateral with NONE of its sides parallel to one other.

3. What are the three names for a trapezoid?

The Scalene Trapezoid is a trapezoid with no equal-sided sides.

  • The two opposing sides of an isosceles trapezoid are parallel, while the two other sides are of equal length. In addition, the diagonals are of the same length.

  • A trapezoid with a right angle is known as a right trapezoid. Properties. It's at a 45-degree angle.

  • Obtuse Trapezoid: There must be two obtuse angles in the trapezoid. One of the legs is perpendicular to the foundations.

  • Sharp Trapezoid: On its longer base edge, it features two consecutive acute angles. It's a trapezoid with the same measure of base angles.

4. How to calculate the area of a trapezoid?

There are two approaches to prove the formula for finding the area of a trapezoid:

  • Using a parallelogram as proof

  • Using a triangle as a proof


Using a triangle, we'll demonstrate how to prove the area of a trapezoid formula. Consider the trapezoid with the bases a and b and the height h shown above. To demonstrate the formula,

  • One of the legs should be divided into two halves.

  • A triangular section of the trapezoid should be cut off.

  • Attach it to the bottom of the figure.


The trapezoid is reorganized into a triangle in this manner. The areas of the trapezoid and the triangle are the same, as we can see in the picture above. We can also observe that the triangle's base is (a + b) and that the triangle's height is h.


The trapezoid's area is equal to the triangle's area.

12 (a + b) h = 12 (a + b) h = 12 (a + b) h = 12 (a + b) h = 12 (a + b) h = 12 (a + b) h = 12 (a + b) h