Worksheet: Area of a Parallelogram

In this worksheet, we will practice calculating the area of a parallelogram and solving word problems requiring the area of parallelogram-shaped figures.

Q1:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram and 𝐸 𝐹 = 6 c m , find its area.

Q2:

Find the area of the parallelogram 𝐴 𝐡 𝐢 𝐷 where 𝐴 𝐡 = 8 . 3 c m .

Q3:

Find the area of a parallelogram having a height of 18 cm and a base length of 12 cm.

  • A 60 cm2
  • B 216 cm2
  • C 1 0 8 cm2
  • D 30 cm2
  • E 432 cm2

Q4:

The given figure shows a parallelogram inside a rectangle. Determine the area inside the rectangle that is not occupied by the parallelogram.

Q5:

The given figure shows one parallelogram inside another. Determine the area of the shaded part.

  • A 2 5 3 1 0 cm2
  • B 2 3 2 5 cm2
  • C 74 cm2
  • D 5 0 3 5 cm2

Q6:

The following figure represents a rectangle inside a parallelogram. What is the area of the colored region?

Q7:

The table shows the dimensions of parallelograms drawn by three students. Whose parallelogram has the largest area?

Student Base ( ) c m Height ( ) c m
James 2 1 2 3 1 5
Jacob 2 1 3 1 2 7
Mason 1 4 9 4 2 9
  • AMason
  • BJames
  • CJacob

Q8:

The figure below represents the design of a rectangular piece of land whose dimensions are 14 m and 9.2 m, where it has three congruent places for parking cars that are in the shape of a parallelogram, two congruent places for planting flowers that are in the shape of a triangle, and a passage for cars that is in the shape of a rectangle whose width is 4.6 m. Determine the total area specified for parking cars and the total area for planting flowers respectively.

  • A parking area = 5 6 . 3 5 m  , garden area = 1 6 . 1 m 
  • B parking area = 4 8 . 3 m  , garden area = 1 6 . 1 m 
  • C parking area = 5 6 . 3 5 m  , garden area = 8 . 0 5 m 
  • D parking area = 4 8 . 3 m  , garden area = 8 . 0 5 m 

Q9:

Find the base length of a parallelogram whose area is 306 cm2 and height is 17 cm.

  • A 2 8 9 cm
  • B 1 8 cm
  • C 2 7 2 cm
  • D 3 6 cm
  • E 5 4 cm

Q10:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram and 𝐷 𝐸 = 1 3 c m , find the length of 𝐷 𝐹 .

Q11:

The lengths of two adjacent sides in a parallelogram are 20 cm and 25 cm. If its greater height is 23 cm, find its smaller height to the nearest centimeter.

Q12:

Given that the area of the parallelogram 𝑋 π‘Œ 𝑍 𝐿 is 682 cm2, find the area of β–³ 𝑀 𝐿 𝑍 .

Q13:

A parallelogram with area 301 has a base of 35. What is its height?

Q14:

Given that the area of the parallelogram 𝑋 π‘Œ 𝑍 𝐿 = 6 1 0 . 9 c m  , find the length of 𝑋 𝐿 .

Q15:

Find the area of the parallelogram 𝐴 𝐡 𝐢 𝐷 .

Q16:

If 𝐢 𝐡 = 2 3 c m , 𝐴 𝐸 = 1 6 c m , and 𝐴 𝐹 = 2 0 c m , find the area of the parallelogram 𝐢 𝐡 𝐴 𝐷 and then determine the length of 𝐢 𝐷 to the nearest hundredth.

  • A area of 𝐢 𝐡 𝐴 𝐷 = 1 6 . 0 0 c m  , 𝐢 𝐷 = 3 2 0 . 0 0 c m
  • B area of 𝐢 𝐡 𝐴 𝐷 = 3 6 8 . 0 0 c m  , 𝐢 𝐷 = 1 8 . 4 0 c m
  • C area of 𝐢 𝐡 𝐴 𝐷 = 3 2 0 . 0 0 c m  , 𝐢 𝐷 = 1 6 . 0 0 c m
  • D area of 𝐢 𝐡 𝐴 𝐷 = 1 8 4 . 0 0 c m  , 𝐢 𝐷 = 1 8 . 4 0 c m
  • E area of 𝐢 𝐡 𝐴 𝐷 = 1 8 . 4 0 c m  , 𝐢 𝐷 = 3 6 8 . 0 0 c m

Q17:

Determine the height of a parallelogram whose area is 20 cm2 and base length is 4 cm.

Q18:

Find the area of the parallelogram 𝐴 𝐡 𝐢 𝐷 , given that 𝐡 𝐹 = 6 . 6 9 cm.

Q19:

Daniel is doing a research project on the nation of Trinidad and Tobago. Part of the project is to paint a replica of the nation’s flag. Determine the area of the black part of the flag.

  • A 8 0 2 9 in2
  • B 1 6 0 4 9 in2
  • C 4 0 1 9 in2
  • D 6 0 1 6 in2

Q20:

Determine the area of the colored part in the shown rectangle that has a parallelogram inside of it.

Q21:

In this wallpaper design, what is the area of the shaded parallelograms?

Q22:

A town requires each parking space to have a minimum area of 169 square feet. Do the measurements of the parking spaces shown meet the requirements? State the area of each parking space.

  • Ayes, 172.5 ft2
  • Byes, 345 ft2
  • Cno, 86.25 ft2
  • Dno, 53 ft2
  • Eno, 26.5 ft2

Q23:

Each parallelogram-shaped piece in the quilt block shown has height 1 2 3 4 inches and base 2 5 1 2 inches. How many square feet of fabric is required for 16 blocks ?

  • A 1,734 ft2
  • B 20,808 ft2
  • C 867 ft2
  • D 1 4 4 1 2 ft2
  • E 7 2 1 4 ft2

Q24:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram whose area is 2,643.21 cm2 and 𝐡 𝐢 = 6 8 . 3 c m , find the length of 𝐴 𝐸 .

Q25:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram of area 61.1 cm2, 𝑋 𝐡 π‘Œ 𝐷 is a rectangle of area 46.06 cm2, and 𝐴 𝑋 = 1 . 6 c m , find the perimeter of the rectangle 𝑋 𝐡 π‘Œ 𝐷 .

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