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Worksheet: Finding the Area of a Parallelogram

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:

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.

  • A 22 cm
  • B 29 cm
  • C 460 cm
  • D 18 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:

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

Q6:

Each parallelogram-shaped piece in the quilt block shown has height 1 4 1 4 inches and base 2 8 1 2 inches. How many square feet of fabric is required for 8 blocks ?

  • A 12 996 ft2
  • B 4 5 1 8 ft2
  • C 1 083 ft2
  • D 9 0 1 4 ft2
  • E 5 4 1 1 2 ft2

Q7:

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

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

Q8:

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
  • BJacob
  • CJames

Q9:

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

Student Base ( ) c m Height ( ) c m
Liam 3 3 8 4 1 3
Daniel 2 1 2 2 1 8
James 4 1 2 3 3 1 0
  • ADaniel
  • BLiam
  • CJames

Q10:

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 = 4 8 . 3 m 2 , garden area = 8 . 0 5 m 2
  • B parking area = 5 6 . 3 5 m 2 , garden area = 8 . 0 5 m 2
  • C parking area = 5 6 . 3 5 m 2 , garden area = 1 6 . 1 m 2
  • D parking area = 4 8 . 3 m 2 , garden area = 1 6 . 1 m 2

Q11:

The figure below represents the design of a rectangular piece of land whose dimensions are 12 m and 7 m, where it has five 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 3.5 m. Determine the total area specified for parking cars and the total area for planting flowers respectively.

  • A parking area = 3 5 m 2 , garden area = 3 . 5 m 2
  • B parking area = 3 8 . 5 m 2 , garden area = 3 . 5 m 2
  • C parking area = 3 8 . 5 m 2 , garden area = 7 m 2
  • D parking area = 3 5 m 2 , garden area = 7 m 2

Q12:

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

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

Q13:

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

Q14:

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

Q15:

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 100 in2
  • B 400 in2
  • C 150 in2
  • D 200 in2

Q16:

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

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

Q17:

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 .

Q18:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram whose area is 313.65 cm2 and 𝐡 𝐢 = 2 0 . 5 c m , find the length of 𝐴 𝐸 .

Q19:

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

Q20:

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

Q21:

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 .

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, 86.25 ft2
  • Cno, 53 ft2
  • Dyes, 172.5 ft2
  • Eno, 26.5 ft2

Q23:

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

Q24:

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

Q25:

Given that the area of the parallelogram 𝐴 𝐡 𝐢 𝐷 is 24 cm2, and the area of the rectangle 𝑋 𝐡 π‘Œ 𝐷 is 12 cm2, find the perimeter of the rectangle 𝑋 𝐡 π‘Œ 𝐷 .