Perimeter of Trapezoid
The perimeter of the trapezoid is the sum of the lengths of each side of the trapezoid. A trapezoid is a twodimensional foursided shape that has two sides parallel to each other and two nonparallel sides termed as bases and legs respectively. Like all twodimensional shapes, you will learn how to calculate the perimeter of the trapezoid. Stay tuned to learn how to use its formula using solved examples!!!
1.  What is the Perimeter of Trapezoid? 
2.  Formula of Perimeter of Trapezoid 
3.  How to Find the Perimeter of Trapezoid? 
4.  FAQs on Perimeter of Trapezoid 
What is the Perimeter of Trapezoid?
The perimeter of a trapezoid is defined as the total length of the boundary of the trapezoid. A trapezoid is one of those quadrilaterals which is an irregular polygon. Thus, the perimeter of the trapezoid is given by summing the lengths of all its sides. Since the trapezoid is a twodimensional shape, thus, the perimeter of the trapezoid will also lie in a twodimensional plane only. The unit of the perimeter of the trapezoid is given as units, where units can be "inches", "feet", "meters" or "centimeters" etc.
Formula of Perimeter of Trapezoid
Consider any trapezoid ABCD where AB and CD are sides parallel to each other (that is, they are bases) while AD and BC are nonparallel sides (that is, they are legs). Let the perimeter of the trapezoid is "P".
The perimeter of trapezoid ABCD is given as P = AB + BC + CD + AD. It can also be written as a sum of lengths of parallel sides and the sum of lengths of nonparallel sides as AB and CD are parallel sides and AD and BC are nonparallel sides. The perimeter of the trapezoid in terms of area is given as P = (sum of the lengths of nonparallel sides) + 2\(\frac{A}{h}\) where A is the area of trapezoid and h is its height.
How to Find the Perimeter of Trapezoid?
The perimeter of the trapezoid can be found by using the following steps:
 Step 1: Write the dimensions of all the sides of the trapezoid.
 Step 2: Add the lengths of all the sides.
 Step 3: Once the value of the perimeter is obtained, write the unit with the value so obtained.
Example: Find the perimeter of a trapezoid whose parallel sides measure 5 units and 7 units while the nonparallel sides measure 3 units and 4 units.
Solution: Given that: The lengths of parallel sides are 5 units and 7 units and lengths of nonparallel sides measure 3 units and 4 units.
Thus, the perimeter of the trapezoid is P = Sum of lengths of parallel sides + Sum of lengths of nonparallel sides ⇒ P = (5 + 7) units + (3 + 4) units. Thus, P = 19 units.
∴ The perimeter of the trapezoid is 19 units.
Solved Examples on Perimeter of Trapezoid

Example 1: Find the perimeter of the trapezoidal park having sides 10 meters, 6 meters, 8 meters, and 9 meters.
Solution: The dimensions of the trapezoidal park are 10 meters, 6 meters, 8 meters, and 9 meters. Thus, the perimeter of the trapezoid (park) is given as:
Perimeter of park = (10 + 6 + 8 + 9) meters. Thus, the perimeter of the trapezoidal park = 33 meters
∴ The perimeter of the trapezoidal park is 33 meters.

Example 2: What is the perimeter of the trapezoid if the sum of lengths of nonparallel sides is 12 units, the height of the trapezoid is 10 units, the length of one of the bases is 5 units and the area is 40 square units?
Solution: Given that sum of lengths of nonparallel sides = 12 units, height of trapezoid = 10 units, length of one base (b) = 5 units, Area of trapezoid = 40 square units. Let the length of the other base is x units and the perimeter of the trapezoid is "P".
As we know, area of trapezoid, A = ½ (a + b) h ⇒ A = ½ (a + b) h = ½ (x + 5) (10) = 40 square units
= 5(x + 5) = 40
= 5x + 25 = 40
= 5x = 40  25 = 15
= 5x = 15 ⇒ x = 3 unitsPerimeter of trapezoid = Sum of lengths of parallel sides + Sum of lengths of nonparallel sides ⇒ P = (x + 5) units + (12) units
Thus, P = (3 + 5) units + 12 units ⇒ P = 20 unitsTherefore, the perimeter of the trapezoid is 20 units.
FAQs on Perimeter of Trapezoid
What is the Perimeter of the Trapezoid?
The total length of the boundary of the trapezoid is referred to as the perimeter of the trapezoid. The perimeter of the trapezoid depends on the lengths of all sides of trapezoid. It can also be expressed in terms of area as P = (sum of the lengths of nonparallel sides) + 2\(\frac{A}{h}\) where A is the area of trapezoid and h is its height.
What is the Formula for Perimeter of Trapezoid?
The formula for the perimeter of the trapezoid is the sum of lengths of all sides of the trapezoid. For any trapezoid ABCD, the perimeter of trapezoid ABCD is given as, P = AB + BC + CD + AD, where AB, CD are parallel sides (bases) and AD, BC are nonparallel sides (legs). Thus, the perimeter of the trapezoid can also be written as P = (sum of lengths of parallel sides) + (sum of lengths of nonparallel sides).
How to Find the Perimeter of Trapezoid?
We can find the perimeter of the trapezoid using the following steps:
 Step 1: Find the lengths of all sides of the trapezoid.
 Step 2: Add the lengths of all the sides of the trapezoid to determine the value of the perimeter of the trapezoid.
 Step 3: Once the value of the perimeter of the trapezoid is obtained, we mention the unit that has to be placed with it.
How Do You Find the Missing Side length If Perimeter of Trapezoid is Given?
We can determine the missing side length of the perimeter of the trapezoid by using the following steps:
 Step 1: Write the given dimensions of the trapezoid.
 Step 2: Assume the missing side length of the trapezoid to be "x" units.
 Step 3: Add the lengths of all the sides of the trapezoid and equate the value to the perimeter of the trapezoid.
 Step 4: Once the equation is obtained, solve for "x" to determine the value of the missing side length of the trapezoid.
How to Find the Perimeter of Trapezoid When the Area of Trapezoid is Given?
We can find the perimeter of the trapezoid when the area of the trapezoid is given using the following steps:
 Step 1: Find the value of the sum of lengths of legs of the trapezoid.
 Step 2: Write the value of height and area of the trapezoid.
 Step 3: Use the formula, P = (sum of the lengths of nonparallel sides) + 2(Area of trapezoid/height of trapezoid) to determine the value of perimeter of the trapezoid.
What Happens to the Perimeter of Trapezoid If All Sides of Trapezoid Are Doubled?
If the lengths of all sides of the trapezoid are doubled, then the perimeter will also get doubled as P = (sum of lengths of parallel sides) + (sum of lengths of nonparallel sides) and the value of each side gets doubled, thereby doubling the value of perimeter.
What Happens to the Perimeter of Trapezoid If the Bases are Doubled?
The perimeter of the trapezoid increases as the bases are doubled thereby increasing the value of the sum of the length of parallel sides which in turn causes the value of the perimeter of the trapezoid to increase but it does not double or quadruple as only a part of the value of perimeter is increased and not the entire value.