Worksheet: Perimeter of a Parallelogram

In this worksheet, we will practice finding the perimeter of a parallelogram and constructing an algebraic expression that indicates this perimeter.

Q1:

Given that 𝐴 𝐵 𝐶 𝐷 is a parallelogram, find 𝑚 𝐷 , 𝑚 𝐴 , and the perimeter of 𝐴 𝐵 𝐶 𝐷 .

  • A 𝑚 𝐷 = 7 2 , 𝑚 𝐴 = 7 2 , perimeter of 𝐴 𝐵 𝐶 𝐷 = 4 1 c m
  • B 𝑚 𝐷 = 1 0 8 , 𝑚 𝐴 = 7 2 , perimeter of 𝐴 𝐵 𝐶 𝐷 = 8 2 c m
  • C 𝑚 𝐷 = 7 2 , 𝑚 𝐴 = 1 0 8 , perimeter of 𝐴 𝐵 𝐶 𝐷 = 4 1 c m
  • D 𝑚 𝐷 = 7 2 , 𝑚 𝐴 = 1 0 8 , perimeter of 𝐴 𝐵 𝐶 𝐷 = 8 2 c m

Q2:

In the figure below, both 𝐴 𝐵 𝐶 𝐷 and 𝐻 𝐵 𝐶 𝑂 are parallelograms, and the perimeter of 𝐴 𝐵 𝐶 𝐷 is 55.4 cm. Find the length of 𝑂 𝐻 .

Q3:

Given a rectangle with sides 8 and 3, and a parallelogram with sides 2 and 5, what is the difference in their perimeters?

Q4:

The lengths of two adjacent sides of a parallelogram are 8 𝑡 units and 8 𝑐 units. Write an expression for its perimeter.

  • A 2 ( 𝑡 + 𝑐 ) units
  • B ( 8 𝑡 + 8 𝑐 ) units
  • C ( 1 6 𝑡 + 8 𝑐 ) units
  • D 2 ( 8 𝑡 + 8 𝑐 ) units
  • E ( 8 𝑡 + 1 6 𝑐 ) units

Q5:

𝐴 𝐵 𝐶 𝐷 is a parallelogram. Given that the perimeter of 𝐴 𝐵 𝐶 𝐷 is 54, find the length of 𝐴 𝐵 .

Q6:

Calculate the perimeter of a parallelogram having side lengths of 39 cm and 5 cm.

Q7:

One side of a parallelogram is 2, and its perimeter is 70. Determine the length of the other side.

Q8:

Given that 𝐴 𝐵 𝐶 𝐷 is a parallelogram, and the perimeter of 𝐵 𝐸 𝐶 is 178 cm, determine the length of 𝐸 𝐶 .

Q9:

𝐴 𝐵 𝐶 𝐷 is a parallelogram. Given that the perimeter of 𝐴 𝐵 𝐶 𝐷 is 88, find the length of 𝐴 𝐵 .

Q10:

𝐴 𝐵 𝐶 𝐷 is a parallelogram. Given that the perimeter of 𝐴 𝐵 𝐶 𝐷 is 170, find the length of 𝐴 𝐵 .

Q11:

𝐴 𝐵 𝐶 𝐷 is a parallelogram. Given that the perimeter of 𝐴 𝐵 𝐶 𝐷 is 128, find the length of 𝐴 𝐵 .

Q12:

Given a rectangle with sides 5 and 8, and a parallelogram with sides 7 and 5, what is the difference in their perimeters?

Q13:

Given that 𝐴 𝐵 𝐶 𝐷 is a parallelogram, find 𝑚 𝐷 , 𝑚 𝐴 , and the perimeter of 𝐴 𝐵 𝐶 𝐷 .

  • A 𝑚 𝐷 = 1 1 3 , 𝑚 𝐴 = 1 1 3 , perimeter of 𝐴 𝐵 𝐶 𝐷 = 2 2 c m
  • B 𝑚 𝐷 = 6 7 , 𝑚 𝐴 = 1 1 3 , perimeter of 𝐴 𝐵 𝐶 𝐷 = 4 4 c m
  • C 𝑚 𝐷 = 1 1 3 , 𝑚 𝐴 = 6 7 , perimeter of 𝐴 𝐵 𝐶 𝐷 = 2 2 c m
  • D 𝑚 𝐷 = 1 1 3 , 𝑚 𝐴 = 6 7 , perimeter of 𝐴 𝐵 𝐶 𝐷 = 4 4 c m

Q14:

In the figure below, both 𝐴 𝐵 𝐶 𝐷 and 𝐻 𝐵 𝐶 𝑂 are parallelograms, and the perimeter of 𝐴 𝐵 𝐶 𝐷 is 26.2 cm. Find the length of 𝑂 𝐻 .

Q15:

Calculate the perimeter of a parallelogram having side lengths of 10 cm and 6 cm.

Q16:

Calculate the perimeter of a parallelogram having side lengths of 47 cm and 31 cm.

Q17:

The lengths of two adjacent sides of a parallelogram are 9 𝑏 units and 9 𝑦 units. Write an expression for its perimeter.

  • A 2 ( 𝑏 + 𝑦 ) units
  • B ( 9 𝑏 + 9 𝑦 ) units
  • C ( 1 8 𝑏 + 9 𝑦 ) units
  • D 2 ( 9 𝑏 + 9 𝑦 ) units
  • E ( 9 𝑏 + 1 8 𝑦 ) units

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