# 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 is a parallelogram and , find its area.

Q2:

Find the area of the parallelogram where .

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 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 cm2
• B cm2
• C 74 cm2
• D 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 , garden area
• B parking area , garden area
• C parking area , garden area
• D parking area , garden area

Q9:

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

• A cm
• B cm
• C cm
• D cm
• E cm

Q10:

Given that is a parallelogram and , find the length of .

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 is 682 cm2, find the area of .

Q13:

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

Q14:

Given that the area of the parallelogram , find the length of .

Q15:

Find the area of the parallelogram .

Q16:

If , , and , find the area of the parallelogram and then determine the length of to the nearest hundredth.

• A area of ,
• B area of ,
• C area of ,
• D area of ,
• E area of ,

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 , given that 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 in2
• B in2
• C in2
• D 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 inches and base inches. How many square feet of fabric is required for 16 blocks ?

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

Q24:

Given that is a parallelogram whose area is 2,643.21 cm2 and , find the length of .

Q25:

Given that is a parallelogram of area 61.1 cm2, is a rectangle of area 46.06 cm2, and , find the perimeter of the rectangle .