Worksheet: Applications of Perimeters of Squares and Rectangles

In this worksheet, we will practice calculating the perimeter of rectangular- or square-shaped real-life objects, such as gardens, frames, rooms, etc.

Q1:

A rectangular field with dimensions 68 m and 43 m is surrounded by a fence. The field contains a square playground with side length 13 m that also has a fence around it. Calculate the total length of fence around the field and the playground.

Q2:

If a rectangle-shaped keyboard has dimensions of 45 cm by 150 mm, what is its perimeter in centimetres?

Q3:

A square carpet has a side length of 10 m, and a rectangular carpet has a length of 13 m. Given that the two carpets have the same perimeter, find the width of the rectangular carpet.

Q4:

Rania is building a fence around her rectangular garden. The garden is 43 feet wide and 56 feet long. Fences can only be bought in sections that are 18 feet long, but they can be cut to size after purchase. How many sections does she need to buy?

Q5:

The Parkers are building a fence around their rectangular yard that is 52 feet long and 29 feet wide. How much fence will they need?

Q6:

A fence around a rectangular garden has a length of 164 feet and a width of 109 feet. Determine the length of the fence.

Q7:

The perimeter of a square is 108 cm. A smaller square has side lengths that are 9 cm shorter than the sides of the first square. Find the perimeter of the smaller square.

Q8:

Determine the perimeter of the shape below.

Q9:

I want to draw a rectangle with perimeter 6 cm on this grid and each corner of the rectangle must be at one of the dots. How many rectangles like this can I draw?

Q10:

Sally has a 64-feet-long fence around her garden. If her garden is in the shape of a square, determine the length of each side.

Q11:

Ethan wants to add fringes to all the sides of a rectangular rug for her bedroom. Given that the rug is 4.5 feet wide and 5 feet long, determine how many feet of fringe she needs.

Q12:

The given diagram shows the floor plan of the Karim’s house. Which of the rectangular rooms has the greatest perimeter?

  • AEngy’s bedroom
  • BSameh’s bedroom
  • Cthe living room
  • DKarim’s bedroom
  • Ethe kitchen

Q13:

Benjamin’s back yard measures 46 by 29 feet, while his front yard is a square with a side length of 38 feet. If Benjamin decides to fence both of them, determine the length of the fencing he will need to do so.

Q14:

How many rectangles can be drawn in the given grid, such that the vertices of each rectangle coincide with four of the dots and that each rectangle’s perimeter equals 8 cm?

Q15:

A rectangular park has dimensions of 150 by 93 feet. There is a 3-foot-wide sidewalk that borders each side of this park. What is the outer perimeter of the sidewalk that encloses the neighborhood park?

Q16:

Determine the perimeter of a poster that is 47 inches long and 30 inches wide.

Q17:

A man has a square-shaped garden with length 16 metres that he wants to surround with a fence. If one metre of the fence costs 7 LE, how much will the fence cost?

  • A112 LE
  • B64 LE
  • C224 LE
  • D448 LE

Q18:

A square ballet studio has an area of 784 square feet. A carpenter has been asked to instal a barre around the perimeter of the studio. What is the total length of the barre?

  • A 56 ft
  • B 28 ft
  • C 32 ft
  • D 112 ft
  • E 30 ft

Q19:

A frame needs to be designed for a rectangular picture whose dimensions are 35 cm and 15 cm. Given that the frame costs 3 LE per metre, find the cost of the frame.

Q20:

Calculate, in decimetres, the length of a rectangle whose perimeter is 190 cm and width is 35 cm.

Q21:

The perimeter of a rectangle is 16 cm. If the length is 𝑥 cm, write an expression for the width.

  • A ( 𝑥 1 6 ) cm
  • B ( 8 + 𝑥 ) cm
  • C ( 1 6 𝑥 ) cm
  • D ( 8 𝑥 ) cm

Q22:

The width of a rectangle is 𝑥 cm and its length is twice its width. Write an expression for its perimeter in cm.

  • A ( 4 + 2 𝑥 ) cm
  • B ( 6 + 2 𝑥 ) cm
  • C 4 𝑥 cm
  • D 6 𝑥 cm

Q23:

Write an expression that represents the perimeter of a rectangle having a width 𝑤 and a length that is one unit more than 4 times the width.

  • A 2 𝑤 + 2
  • B 1 0 𝑤
  • C 5 𝑤 + 1
  • D 1 0 𝑤 + 2
  • E 9 𝑤 + 1

Q24:

A rectangle has width 𝑤 and length 𝑙 . A new rectangle is formed which has the same length but double the width. Find the perimeter 𝑃 and area 𝐴 of this new rectangle.

  • A 𝑃 = 𝑙 + 2 𝑤 , 𝐴 = 4 𝑙 𝑤
  • B 𝑃 = 2 𝑙 + 2 𝑤 , 𝐴 = 𝑙 𝑤
  • C 𝑃 = 2 𝑙 + 𝑤 , 𝐴 = 1 2 𝑙 𝑤
  • D 𝑃 = 2 𝑙 + 4 𝑤 , 𝐴 = 2 𝑙 𝑤
  • E 𝑃 = 𝑙 + 𝑤 , 𝐴 = 3 𝑙 𝑤

Q25:

The length of a rectangle is 𝑥 cm and its width is 12 cm. Write an expression for its perimeter in centimeters.

  • A ( 1 2 + 𝑥 ) cm
  • B 1 2 𝑥 cm
  • C 2 4 𝑥 cm
  • D ( 2 4 + 2 𝑥 ) cm

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