Lesson Worksheet: Areas of Rectangles and Squares Mathematics • 6th Grade

In this worksheet, we will practice finding the areas of rectangles and squares using a formula with fractions and decimals and solving real-life problems.

Q1:

Find the area of a rectangle whose length is 4 times its width, if its width is 4 cm.

Q2:

Given that 𝐴𝐡𝐢𝐷 is a rectangle of area 1,389.6 cm2, find the area of figure 𝐴𝐹𝐷𝐸.

Q3:

Jackson parked his rectangular car in an empty rectangular parking lot. The dimensions of the parking lot are 87 feet by 83 feet and the dimensions of the car are 18 feet by 8 feet. What area of the parking lot is still empty?

Q4:

A rectangular carpet measuring 4 m by 3 m is placed in a square room of length 9 m. What area of the floor is not covered by the carpet?

Q5:

If a square and a rectangle have equal area, and the rectangle measures 18 cm by 50 cm, what is the length of the square?

Q6:

The size of youth soccer fields depends on the age group of the players. Use the table to determine the difference between the area of a soccer field for under 14s compared to the field for under 12s.

Age GroupUnder 10sUnder 12sUnder 14s
Field Length (Yards)7080100
Field Width (Yards) 40 50 60

Q7:

Michael wants to pave a section of his yard that is 16 m long and 3 m wide. If paving one square meter will cost 9 LE, calculate the total cost.

Q8:

Jennifer’s rectangular patio is 45 feet long and covers 1,575 square feet. She wants to fence all but one of the shorter sides. How much fencing does she need?

Q9:

A 2-inch-wide rectangular frame surrounds a painting that is 9 inches wide and 12 inches tall. What is the area of the frame?

Q10:

A family is planning to have a rectangular swimming pool in their backyard. The pool will be 19 ft by 13 ft. Given that they also plan on having a ceramic walkway around the pool, which should be 8 ft wide, determine the area of the walkway.

Q11:

A gymnasium floor that is 50 ft wide and 84 ft long needs to be refinished. If the cost for refinishing is $14 per square foot, determine the total cost.

Q12:

If the length of every side of a rectangle is increased by 6 units, would its area increase by 36 square units?

  • AYes
  • BNo

Q13:

A rectangle with an area of 196 square feet is 4 times as long as it is wide. Find its length and width.

  • Alength = 7 ft, width = 1.8 ft
  • Blength = 78.4 ft, width = 19.6 ft
  • Clength = 56 ft, width = 14 ft
  • Dlength = 98 ft, width = 24.5 ft
  • Elength = 28 ft, width = 7 ft

Q14:

The figure represents two shelves used to display toys in a store. Shelf 1 is large enough for 4 toys. For every additional square foot of area a shelf has, it can hold one more toy. How many toys can shelf 2 hold?

Q15:

The student committee in a school are building a stage in the gym for the upcoming prom. The stage is 16 feet long and 10 feet wide, and the gym is 30 feet by 27 feet. How many square feet of open space will be left after the stage is completed?

Q16:

Sophia’s garden is 14 by 15 feet. If she extends the length of each side by 7 feet, by how many square feet will the area increase?

Q17:

In the figure, π΄π‘Š=𝐡𝑋=πΆπ‘Œ=𝐷𝑍. Given that the areas of the squares 𝐴𝐡𝐢𝐷 and π‘Šπ‘‹π‘Œπ‘ are 324 cm2 and 1,314 cm2 respectively, find the length of 𝐷𝑍.

Q18:

Given that three-quarters of the area of a square is 341164 m2, calculate its side length.

  • A4631 m
  • B316 m
  • C274 m
  • D34 m

Q19:

The length of a rectangle is 13 cm more than its width. The rectangle’s area is 48 cm2. What is its length?

Q20:

Given that the area of the rectangle 𝐴𝐡𝐢𝐷 is 56 cm2, find the length of 𝐡𝐢.

Q21:

Given that the length of a rectangle is 2 times its width, and its perimeter is 114 cm, find its area.

Q22:

Find the missing side of the rectangle in centimeters, knowing that its area is 0.285 m2.

Q23:

The width of a rectangle is 12 of its length. If the length of the rectangle is 14 cm, find the width and area of the rectangle.

  • Awidth =7 cm, area =98 cm2
  • Bwidth =7 cm, area =42 cm2
  • Cwidth =7 cm, area =21 cm2
  • Dwidth =8 cm, area =112 cm2
  • Ewidth =98 cm, area =7 cm2

Q24:

David wants to carpet a room measuring 9 by 12 meters. Determine the amount of carpet needed.

Q25:

What is the area of a rectangle of width 7 and length 25?

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