How to find the Perimeter of a Trapezoid?
Last Updated :
23 Jul, 2025
Answer: To find the Perimeter of a Trapezoid, add the Lengths of all four sides.
Perimeter = a + b + c + d
Where:
- a and b are the lengths of the parallel sides,
- c and d are the lengths of the non-parallel sides.
Note:
In India, the shape with one pair of parallel sides is called a trapezium but in the USA, the same shape is called a trapezoid.
This difference is due to variations between British and American English in mathematical terminology.
For Example, consider the trapezoid ABCD. 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.
To find the perimeter, use the formula:
P = AB + BC + CD + D
The perimeter can also be expressed as:
- The sum of the lengths of parallel sides: AB + CD
- The sum of the lengths of non-parallel sides: AD + BC
What is a Trapezoid?
A 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.
The 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 lengths are a, b, c, and d then its perimeter is,
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The image added above is a trapezoid with sides a, b, c, and d.
Perimeter of Trapezoid(P) = Sum of All 4 Sides of Trapezoid
P = AB + BC + CD + DA
Steps to Find the 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 in 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
Step 1: If we take the △QUR, we get QU = 80m and UR = 70m. We can see that △QUR 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 △PSV, 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,
Solved 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 bases of 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.
Related Articles:
Practice Questions on Perimeter of Trapezoid
Question 1: Find the perimeter of the trapezoid with base sides 8 cm and 22 cm and non-parallel sides 11 cm and 19 cm.
Question 2: Find the perimeter of the trapezoid with base sides 12 cm and 20 cm and non-parallel sides 21 cm and 19 cm.
Question 3: Find the perimeter of the isosceles trapezoid with a parallel base of 2 cm and 3 cm and equal sides, 7 cm.
Question 4: Find the perimeter of the isosceles trapezoid with parallel bases of 10 cm and 11 cm and equal sides, of 12 cm.
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