Worksheet: Areas of Rectangles and Squares

In this worksheet, we will practice finding the areas of squares, rectangles, and composite figures.

Q1:

What is the difference in area between a square of side 6 and a rectangle that is 1 by 6?

  • A10
  • B15
  • C60
  • D30
  • E35

Q2:

Given that 𝐴 𝐡 𝐢 𝐷 is a rectangle, π‘Š 𝑋 π‘Œ 𝑍 is a square, 𝐴 𝐡 = 6 c m , and 𝐡 𝐢 = 3 c m , calculate the area of the shaded part.

  • A 18 cm2
  • B 9 cm2
  • C 6 cm2
  • D 13.5 cm2
  • E 4.5 cm2

Q3:

Calculate the area of the grey part.

Q4:

Calculate the area of the shaded part of the figure, given that the inner rectangle measures 6 cm by 8 cm.

Q5:

A rectangle has dimensions of 19 cm and 6 cm, and a square has a side length of 10 cm. Which of the following statements is correct?

  • AThe area of the rectangle is half the area of the square.
  • BThe area of the rectangle is equal to the area of the square.
  • CThe sum of both areas is twice their difference.
  • DThe area of the rectangle is larger than the area of the square.

Q6:

Find the area of a rectangle whose length is 7 times its width, if its width is 50 cm.

Q7:

Given that 𝐴 𝐡 𝐢 𝐷 is a rectangle of area 1β€Žβ€‰β€Ž389.6 cm2, find the area of figure 𝐴 𝐹 𝐷 𝐸 .

Q8:

Karim 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?

Q9:

The figure shows a square with length 3 yards inside a rectangle. Determine the area of the shaded part.

Q10:

Given that the two white rectangles are identical, calculate the area of the coloured region.

  • A 382.5 yd2
  • B 765 yd2
  • C 738 yd2
  • D 630 yd2
  • E 450 yd2

Q11:

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?

Q12:

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?

Q13:

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 Group Under 10s Under 12s Under 14s
Field Length (Yards) 70 80 100
Field Width (Yards) 40 50 60

Q14:

A goat has been tethered to the outside corner of a storehouse by a 5-yard rope. The storehouse has a rectangular base of width 3 yards and length 4 yards. Work out the area of grass that the goat can reach. Give your answer in terms of πœ‹ .

  • A 1 5 πœ‹ square yards
  • B 1 2 πœ‹ square yards
  • C 2 5 πœ‹ square yards
  • D 2 0 πœ‹ s q u a r e y a r d s
  • E 3 5 πœ‹ square yards

Q15:

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

Q16:

Engy has found a new car she would like to purchase. But before she can buy it, she needs to find the area of her garage to check whether the new car will fit. The garage is 18 feet long and 9 feet wide. What is the area?

Q17:

Sally’s rectangular patio is 45 feet long and covers 1β€Žβ€‰β€Ž575 square feet. She wants to fence all but one of the shorter sides. How much fencing does she need?

Q18:

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?

Q19:

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.

Q20:

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.

Q21:

Farida’s quilt has an area of 24 ft2. The length measures 8 ft. What is its width?

Q22:

A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 378 ft2. Find the width of the walkway if the garden is 12 ft wide by 15 ft long.

Q23:

A new space shuttle launchpad is being designed. One piece of the launchpad has an area of 108 square feet. The length measures 12 feet. What does the width measure?

Q24:

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

  • Ano
  • Byes

Q25:

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

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