Perimeter of Trapezoid

The perimeter of a trapezoid is the sum of the lengths of each side of the trapezoid. A trapezoid is a quadrilateral that has two sides parallel to each other and two non-parallel sides termed as bases and legs respectively. Let us learn how to calculate the perimeter of the trapezoid in this article.

The perimeter of a trapezoid is defined as the total length of the boundary of the trapezoid. A trapezoid is a two-dimensional shape (2D shape) and an irregular polygon. Thus, the perimeter of the trapezoid is calculated by adding the length of all its sides. The perimeter of a trapezoid is expressed in linear units like, 'inches', 'feet', 'meters' or 'centimeters', etc.

The formula of the perimeter of a trapezoid is a simple one in which the length of all 4 sides is added. Observe the trapezoid ABCD given below in which sides AB and CD (bases) are parallel to each other while AD and BC (legs) are non-parallel sides.

The perimeter of trapezoid ABCD can be calculated using the formula, Perimeter (P) = AB + BC + CD + DA. It can also be written as a sum of lengths of parallel sides and the sum of lengths of non-parallel sides where AB and CD are the parallel sides and AD and BC are the non-parallel sides.

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 length of all the sides.
• Step 3: Once the value of the perimeter is obtained, write the unit with the value thus obtained.

Example: Find the perimeter of a trapezoid whose parallel sides measure 5 units and 7 units while the non-parallel sides measure 3 units and 4 units.
Solution: Given, the lengths of parallel sides are 5 units and 7 units, and lengths of non-parallel sides measure 3 units and 4 units.
Thus, the perimeter of the trapezoid is P = Sum of lengths of all sides

⇒ P = (5 + 7 + 3 + 4)

Therefore, P = 19 units.

∴ The perimeter of the trapezoid is 19 units.

Perimeter of Trapezoid with Missing Side

The perimeter of a trapezoid can be calculated even if there is a missing side. In such cases, we use the given sides of the trapezoid and apply the Pythagoras theorem and other properties to find the missing side and then the perimeter can be calculated. Let us understand this with the help of an example.

Example: Find the perimeter of a trapezoid ABCD if its dimensions are given as follows: AB = 120 m, DE = 50 m, EF = 120 m, FC = 80 m, BF = 90 m.

Solution: Using the given dimensions, we can find the missing sides AD and BC.

• Step 1: If we take triangle BFC, it is given that BF = 90 m and FC = 80 m. We can see that BFC is a right-angled triangle. So, we can calculate the value of BC using the Pythagoras theorem.
• Step 2: According to the Pythagoras theorem, BC² = BF² + FC². This means, BC² = 90² + 80². Therefore, BC² = 8100 + 6400 ⇒ BC = √14500 = 120.41 m
• Step 3: Since BF = 90 m, AE will also be equal to 90 m because AB is parallel to DC. Now, we can calculate the missing side AD of the trapezoid.
• Step 4: If we take the right angled triangle ADE, we know that AE = 90 m, DE = 50 m. So, after applying the Pythagoras theorem, we get AD² = AE² + DE². This means, AD² = 90² + 50². Therefore, AD² = 8100 + 2500 ⇒ AD = √10600 = 102.9 m.
• Step 5: Now, that we know all the sides of the trapezoid, we can find its perimeter by adding all the 4 sides. This means, Perimeter of trapezoid ABCD = AB + BC + CD + DE ⇒ 120 + 120.41 + 250 + 102.9 = 593.31 m. Therefore, the perimeter of the trapezoid is 593.31 m.

☛ Related Articles

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• Area 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 length of all its sides and it is expressed in linear units.

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 expressed as, P = AB + BC + CD + AD, where AB, CD are parallel sides (bases) and AD, BC are non-parallel sides (legs). Thus, the perimeter of the trapezoid can also be written as P = (sum of lengths of parallel sides) + (sum of lengths of non-parallel sides).

How to Find the Perimeter of Trapezoid?

We can find the perimeter of the trapezoid using the following steps:

• Step 1: Find the length of all the 4 sides of the trapezoid.
• Step 2: Add the lengths of all the sides of the trapezoid to get 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 to Find the Missing Side Length if Perimeter of Trapezoid is Given?

We can find the missing side length of a trapezoid if the perimeter is given. Let us understand this with an example.

Example: If the perimeter of a trapezoid is 24 units and the rest of its sides are given as follows: 5 units, 7 units, 4 units, let us find the missing side.

• Step 1: Write the given dimensions of the trapezoid. Perimeter = 24 units, Side 1 = 5 units, Side 2 = 7 units, Side 3 = 4 units.
• 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. Here, it will be written as, 24 = 5 + 7 + 4 + x
• Step 4: Once the equation is formed, solve for 'x' to get the value of the missing side length of the trapezoid. After solving for the value of 'x', we get, x = 24 - 16 = 8 units. Therefore, the length of the missing side is 8 units.

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 non-parallel sides) and the value of each side gets doubled, thereby doubling the value of perimeter.

How to find the Perimeter of an Isosceles Trapezoid?

The perimeter of an isosceles trapezoid can be calculated in the same way as we find the perimeter of an ordinary trapezoid. However, in an isosceles trapezoid, the legs are of the same length, therefore, it becomes easier to find the perimeter. In this case, the perimeter can be calculated using the formula, Perimeter of trapezoid = a + b + 2c; where 'a' and 'b' are the parallel sides and c is the leg of the trapezoid. Since the two legs are equal in length we represent them as c + c = 2c in the formula.