The parallelogram

The parallelogram

The perimeter of a parallelogram is obtained by adding the lengths of all its sides. Study the following parallelogram with sides a, b, c and d:

Perimeter of a parallelogram = a + b + c + d.

Since the opposite sides of a parallelogram are equal, sides a and c are equal and sides b and d are also equal. That is, a = c and b = d.

Thus, the formula for finding perimeter of the parallelogram can be written as follows:

Perimeter of a parallelogram = a + a + b + b

= 2a + 2b

= 2 (a + b)

Therefore, the perimeter of a parallelogram = 2 (a + b).

Example 1

Find the perimeter of the following parallelogram:

Solution

Given a = 9 cm, b = 6 cm, c = 9 cm and d = 6 cm

Perimeter of a parallelogram = a + b + c + d

= 9 cm + 6 cm + 9 cm + 6 cm

= 30 cm

Therefore, the perimeter of the parallelogram is 30 cm.

Also, you can find the perimeter of a parallelogram by using the formula.

Perimeter of a parallelogram = 2(a + b)

= 2 (9 cm + 6 cm)

= 2 × 15 cm

= 30 cm

Therefore, the perimeter of a parallelogram is 30 cm.

Example 2

Find the perimeter of the following parallelogram:

Solution

Perimeter of a parallelogram = 2(a + b)

= 2 (20 cm + 32 cm)

= 2 × 52 cm

= 104 cm

Therefore, the perimeter of the parallelogram is 104 cm.