Worksheet: Area of a Parallelogram

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

Q1:

Given that 𝐴𝐡𝐢𝐷 is a parallelogram and 𝐸𝐹=6cm, find its area.

Q2:

Find the area of the parallelogram 𝐴𝐡𝐢𝐷 where 𝐴𝐡=8.3cm.

Q3:

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

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.

  • A74 cm2
  • B5035 cm2
  • C25310 cm2
  • D2325 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?

StudentBase ()cmHeight ()cm
James212315
Jacob213127
Mason149429
  • AJacob
  • BMason
  • CJames

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.

  • Aparking area =56.35m, garden area =16.1m
  • Bparking area =48.3m, garden area =16.1m
  • Cparking area =48.3m, garden area =8.05m
  • Dparking area =56.35m, garden area =8.05m

Q9:

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

  • A18 cm
  • B36 cm
  • C54 cm
  • D272 cm
  • E289 cm

Q10:

Given that 𝐴𝐡𝐢𝐷 is a parallelogram and 𝐷𝐸=13cm, find the length of 𝐷𝐹.

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 π‘‹π‘Œπ‘πΏ is 682 cm2, find the area of △𝑀𝐿𝑍.

Q13:

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

Q14:

Given that the area of the parallelogram π‘‹π‘Œπ‘πΏ=610.9cm, find the length of 𝑋𝐿.

Q15:

Find the area of the parallelogram 𝐴𝐡𝐢𝐷.

Q16:

If 𝐢𝐡=23cm, 𝐴𝐸=16cm, and 𝐴𝐹=20cm, find the area of the parallelogram 𝐢𝐡𝐴𝐷 and then determine the length of 𝐢𝐷 to the nearest hundredth.

  • Aarea of 𝐢𝐡𝐴𝐷=16.00cm, 𝐢𝐷=320.00cm
  • Barea of 𝐢𝐡𝐴𝐷=184.00cm, 𝐢𝐷=18.40cm
  • Carea of 𝐢𝐡𝐴𝐷=368.00cm, 𝐢𝐷=18.40cm
  • Darea of 𝐢𝐡𝐴𝐷=18.40cm, 𝐢𝐷=368.00cm
  • Earea of 𝐢𝐡𝐴𝐷=320.00cm, 𝐢𝐷=16.00cm

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 𝐴𝐡𝐢𝐷, given that 𝐡𝐹=6.69 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.

  • A4019 in2
  • B6016 in2
  • C8029 in2
  • D16049 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, 345 ft2
  • BNo, 53 ft2
  • CNo, 26.5 ft2
  • DNo, 86.25 ft2
  • EYes, 172.5 ft2

Q23:

Each parallelogram-shaped piece in the quilt block shown has height 1234 inches and base 2512 inches. How many square feet of fabric is required for 16 blocks ?

  • A20,808 ft2
  • B7214 ft2
  • C1,734 ft2
  • D867 ft2
  • E14412 ft2

Q24:

Given that 𝐴𝐡𝐢𝐷 is a parallelogram whose area is 2,643.21 cm2 and 𝐡𝐢=68.3cm, find the length of 𝐴𝐸.

Q25:

Given that 𝐴𝐡𝐢𝐷 is a parallelogram of area 61.1 cm2, π‘‹π΅π‘Œπ· is a rectangle of area 46.06 cm2, and 𝐴𝑋=1.6cm, find the perimeter of the rectangle π‘‹π΅π‘Œπ·.

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