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How to find the Perimeter of a Trapezoid?

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Perimeter of the Trapezoid in Geometry is the sum of all the sides of the trapezoid. It is the length of all its boundaries and is measured in units of length, i.e. perimeter of the trapezoid is measured in cm, m, etc. A trapezoid is a quadrilateral that has a pair of parallel sides (lines). It is a quadrilateral whose perimeter is the sum of all the sides of a quadrilateral.

Here, in this article, we will learn about, What is a Trapezoid, the Perimeter of the trapezoid, the perimeter of the trapezoid formula, examples, and others in detail.

What is a Trapezoid?

Trapezoid is a polygon with only one pair of parallel sides. These parallel sides are also called the parallel base of the trapezoid. The other two sides of the trapezoid are not parallel and are called the legs of the trapezoid. One school of mathematics asserts that a trapezoid can have a pair of parallel sides, while another school of mathematics maintains that a trapezoid can have more than one pair of parallel sides. Considering the second definition, a parallelogram is also trapezoidal accordingly. However, the first definition does not consider a parallelogram a trapezoid.

What is the Perimeter Of Trapezoid?

The perimeter of a trapezoid is equal to the sum of the lengths of the sides of the trapezoid. The formula for the perimeter of a trapezoid is as simple as the sum of the lengths of its four sides.

Trapezoid-ABCD

In the trapezoid ABCD above, consider the sides AB and CD (base) are parallel to each other, but sides AD and BC (legs) are sides of the trapezoid that are non – parallel. The perimeter of a trapezoid ABCD can be calculated using the formula perimeter (P) = AB + BC + CD + DA. It can also be expressed as the sum of the lengths of parallel sides and the sum of the lengths of non-parallel sides. where AB and CD are parallel sides and AD and BC are nonparallel sides.

Perimeter of Trapezoid Formula

Perimeter of the trapezoid formula is the sum of all the sides of the trapezoid. The formula that gives the perimeter of the trapezoid is given as,

Suppose we are given a trapezium ABCD whose sides are AB, BC, CD and DA such that its length are a, b, c, and d then its perimeter is,

Trapezium-(1)

The image added above is a trapezoid with side a, b, c, and d.

Perimeter of Trapezoid(P) = Sum of All 4 Sides of Trapezoid

P = AB + BC + CD + DA

How to Find Perimeter of a Trapezoid?

The perimeter of a trapezoid can be calculated by following these steps:

Step 1: Note the dimensions of all sides of the Trapezoid.

Step 2: Add the lengths of all the sides of the Trapezoid.

Step 3: The value obtained is the perimeter of the trapezoid which is measured cm, m, etc.

Example: Find perimeter of the trapezoid if its non parllalel sides are 10 cm, 12 cm and its parallel sides are, 14 cm and 22 cm.

Solution:

Given sides of trapezoid,

  • a = 10 cm
  • b = 12 cm
  • c = 14 cm
  • d = 22 cm

Perimeter of Trapezoid(P) = a + b + c + d

P = 10 + 12 + 14 + 22 = 58 cm

Perimeter of a Trapezoid with a Missing Side

The perimeter of a trapezoid can be calculated even if there are not enough sides. In such cases, you can use the given sides of the trapezoid, apply the Pythagoras theorem and other properties to find the missing sides, and then calculate the perimeter.

Example: Find the perimeter of the trapezoid PQRS with dimensions  PQ = 110 m, SV = 40 m, VU = 110 m, UR = 70 m, QU = 80 m.

Solution

Use the given dimensions to find the missing length of PS and QR

Trapezium-PQRS

Step 1: If we take the â–³QUR, we get QU = 80m and UR = 70m. We can see that â–³QUR is a right-angled triangle. So we can use the Pythagoras theorem to calculate the QR value.

Step 2: According to the Pythagoras theorem, QR2 = QU2 + UR2. This means

QR2 = 802 + 702

QR2 =  6400 + 4900

QR = √11300 = 106.301 m

Step 3: Since QU = 80m,  PQ is parallel to SR, so PV is also 80m, so we can now calculate the missing side PS of the trapezoid. 

Step 4: Taking the right triangle â–³PSV,  PV = 80m, SV = 40m, so applying the Pythagoras theorem we get PS2 = PV2 + SV2. This means

PS2 = 802 + 402

PS2 = 6400 + 1600

PS = √8000 = 89.44 m  

Step 5: Now that we know all the faces of the trapezoid, we can add up all four faces to find the perimeter. This means that the perimeter of the trapezoid is PQRS

= PQ + QR + RS + SP

= 110 + 106.301 + 220 + 89.44

= 525.741 m

Thus, the missing side of the trapezoid is found.

Read More,

Examples on Perimeter of Trapezoid

Example 1: If the perimeter of the trapezoid is 60 units and the three sides are 10 units, 25 units, and 12 units, respectively, use the trapezoidal formula to find the size of the fourth side.

Solution:

Given,

  • Perimeter of Trapezoid = 60 units
  • Length of side 1 of Trapezoid =10 units 
  • Length of side 2 of Trapezoid = 25 units
  • Length of side 3 of Trapezoid = 12 units

Let d units be the length of fourth side of trapezoid,

Using Trapezoid Formula,

Perimeter of Trapezoid = Sum of All Sides of Trapezoid 

60 = 10 + 25 + 12 + d

60 = 47 + d

d = 13 units

Example 2: Find the perimeter of the isosceles trapezoid with parallel base 12 cm and 20 cm and equal sides, 9 cm.

Solution:

Given,

  • First Side of Trapezoid(a) = 12 cm
  • Second Side of Trapezoid(b) = 20 cm
  • Equal side of Trapezoid(c) = 9 cm

Perimeter of Isosceles Trapezoid(P) = a + b + c + c

P = 12 + 20 + 9 + 9

P = 50 cm

Thus, the perimeter of the trapezoid is 50 cm

Practice Questions on Perimeter of Trapezoid

Q1. Find the perimeter of the trapezoid with base sides 8 cm and 22 cm and non parallel sides 11 cm and 19 cm.

Q2. Find the perimeter of the trapezoid with base sides 12 cm and 20 cm and non parallel sides 21 cm and 19 cm.

Q3. Find the perimeter of the isosceles trapezoid with parallel base 2 cm and 3 cm and equal sides, 7 cm.

Q4. Find the perimeter of the isosceles trapezoid with parallel base 10 cm and 11 cm and equal sides, 12 cm.

Perimeter of Trapezoid – FAQs

1. What is a Trapezoid?

A trapezoid is a quadrilateral which have a pair of parallel line. It is an other name given ti the trapezium.

2. Define Perimeter of Trapezoid.

Perimeter of the Trapezoid is the sum of all the boundires of the trapezoid. It is also called the sum of all the sides of the trapezoid.

3. What is Perimeter of Trapezoid Formula?

The perimeter of the trapezoid formula is,

Perimeter of Trapezoid = (a + b + c + d) units

where a, b, c, and d are the sides of the trapezoid

4. What is Perimeter of Iscosceles Trapezoid?

Perimeter of the Iscosceles Trapezoid is the sum of all the sides isosceles trapezoid. In an isosceles trapezoid we have two legs of the trapezoid as equal.

Perimeter of Iscosceles Trapezoid = (a + b + 2c) units

where,

  • a and b are parallel sides of the Trapezoid
  • c is the Isosceles Trapezoid

5. What is the Formula and Area of Trapezoid?

Area of Trapezoid is the area inclosed by the sides of the trapezoid and is given using the formula,

Area of Trapezoid = 1/2 × (a + b) × h square units

6. What is a Formula of Trapezium?

In a trapezoid of sides, a, b, c, and d and height h. The trapezim formulas are,

  • Perimeter of Trapezoid = (a + b + c + d)
  • Area of Trapezoid = 1/2(a + b)h

7. How to Find the Perimeter of a Trapezoid?

To find the Perimeter of a Trapezoid, we need to add all the measurement of four sides of a Trapezium.



Last Updated : 16 Oct, 2023
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