Perimeter of a Trapezoid Formula

Quadrilaterals can be defined as, types of polygons that have four sides, four vertices, and four angles along with a pair of diagonals. The Sum of interior angles of quadrilaterals is 360°. There are various kinds of quadrilaterals. As the name itself suggest the word is a combination of two Latin words ‘Quadri‘ means a variant of four, and ‘latus‘ means side.

A trapezoid is a type of quadrilateral that has 4 sides with at least one parallel side in a two-dimensional plane. The parallel sides are called the bases of the trapezoid and the other two sides which are not parallel are referred to as the legs. There can also be two pairs of bases.

Consider the length of the 4 sides are a, b, c, and d.

Perimeter: The sum of all sides of the Trapezoid is known as the perimeter of a Trapezoid.

Perimeter, P = a+b+c+d

Sample Problems

Question 1: If a = 2, b = 3, c = 8 and d = 4. Find the perimeter of Trapezoid.

Solution:

We know that perimeter of Trapezoid is a+b+c+d, so substitute above values into it

2+3+8+4=>17 cm

Therefore, perimeter of Trapezoid is 17 cm.

Question 2: If a = 2, b = 3, c = 8 and perimeter is 17 cm. Find the other side of Trapezoid.

Solution:

We know that perimeter of Trapezoid is a+b+c+d, and given that  perimeter (p) is 17 cm, a=2, b=3 and c=8.

So put these values in the formula

2 + 3 + 8 + c = 17 

=> 13 + c = 17

=> c = 17 – 13

=> c = 4 

Therefore ,the other side of Trapezoid is 4 cm

Question 3: If two legs of Trapezoid  are 5 cm and 8 cm respectively and other sides are 6 cm and 7 cm. Find the perimeter of the Trapezoid.

Solution:

We know that perimeter of Trapezoid is a+b+c+d, so substitute above values into it

Let the first two legs be a and b and other sides be 6 and 7.

5 + 8 + 6 + 7 => 26 cm

Therefore, perimeter of Trapezoid is 26 cm.

Question 4: If two legs of the cot are 60 cm and 23 cm respectively and other legs are 23 cm and 60 cm. Find the perimeter of the cot.

Solution:

We know that perimeter of Trapezoid is a+b+c+d, so substitute above values into it

first two legs are a and b and other two legs are c and d

60 + 23 + 23 + 60 => 166 cm

Therefore, perimeter of cot is 166 cm.

Question 5: If the sides of a tent are 10, 20, 30, and 25 cm respectively. Find the perimeter of the tent.

Solution:

Tent is in the shape of trapezoid

We know that perimeter of Trapezoid is a+b+c+d, so substitute above values into it

10 + 20 + 30 + 25 => 85 cm

Therefore, perimeter of tent is 85 cm.

Question 6: If the sides of a Trapezoid are 12, 30, 36, and 15 cm respectively. Find the perimeter of the Trapezoid.

Solution:

We know that perimeter of Trapezoid is a+b+c+d, so substitute above values into it

12 + 30 + 36 + 15 => 93 cm

Therefore, perimeter of Trapezoid is 93 cm.