Worksheet: Applications of Area of a Square

In this worksheet, we will practice using the side × side formula to find the area of some square real-life objects, such as tiles, carpets, rooms, etc.

Q1:

The side length of each small square in the grid is one unit.

Find the area of the colored shape.

Q2:

The perimeter of a square measures 32 cm. What is its area?

Q3:

Find the area of the square.

Q4:

What is the area of a square of perimeter 36?

  • A 8 1 2
  • B9
  • C18
  • D81
  • E162

Q5:

The side length of a square is 3.9 cm. Find the area of the square.

  • A 5.85 cm2
  • B 7.8 cm2
  • C 30.42 cm2
  • D 15.21 cm2
  • E 22.815 cm2

Q6:

Nabil has a square tablecloth. One side measures 3 metres. Will it cover his picnic table which has an area of 12 square metres?

  • Ano
  • Byes

Q7:

A square carpet with length 8 m is placed in a square hall with length 10 m. Find the area of the floor not covered by the carpet.

  • A 4 m2
  • B 8 m2
  • C 80 m2
  • D 36 m2

Q8:

The courtyard of a castle is in the shape of a square. Given that one side of the courtyard is 41 feet, determine its area in square feet.

Q9:

A tumbling mat for a gymnastics routine is a square whose sides are 40 feet long. What is the area of the tumbling mat?

Q10:

A landlord wants to replace the old flooring in one of his flats with parquet tiles. He can choose between 20-inch square tiles and 15-inch square tiles. Find the difference between the areas of the two tiles.

  • A 5 in2
  • B 625 in2
  • C 35 in2
  • D 175 in2
  • E 385 in2

Q11:

The largest ring in amateur boxing is a square with an area of 400 square feet. What are the dimensions of the ring?

  • A 12 ft by 12 ft
  • B 40 ft by 40 ft
  • C 200 ft by 200 ft
  • D 20 ft by 20 ft
  • E 15 ft by 15 ft

Q12:

Elizabeth wants to tile the floor of her square kitchen with square tiles that have length 20 cm. If the length of her kitchen is 7 m, how many tiles does she need?

Q13:

What is the area of a square of side 17?

Q14:

If the area of a square is 25 square meters, determine, in centimeters, the length of each side.

Q15:

If the perimeter of a square is 28 m, what is its area in square meters?

Q16:

Determine the perimeter of a square whose area is 841 cm2.

Q17:

Determine the formulas for the perimeter, 𝑃 , and area, 𝐴 , of this square.

  • A 𝑃 = 𝑠 4 , 𝐴 = 4 𝑠
  • B 𝑃 = 4 + 𝑠 , 𝐴 = 𝑠 4
  • C 𝑃 = 2 𝑠 , 𝐴 = 4 + 𝑠
  • D 𝑃 = 4 𝑠 , 𝐴 = 𝑠 2
  • E 𝑃 = 𝑠 2 , 𝐴 = 2 𝑠

Q18:

When the perimeter of a square is doubled, which expression explains what happens to its area?

  • AThe area is halved.
  • BThe area is also doubled.
  • CThe area is quartered.
  • DThe area is quadrupled.

Q19:

What is the perimeter of a square with area 1 2 1 4 𝑥 ?

  • A 22
  • B 1 1 2 𝑥
  • C 1 1 2
  • D 2 2 𝑥
  • E 2 2 𝑥

Q20:

A farmer has 5 3 1 3 feet of fencing and wants to build a square pen for his chickens. What is the area of the largest pen he can build?

  • A 2 6 2 3 ft2
  • B 1 3 1 3 ft2
  • C 5 3 1 3 ft2
  • D 1 7 7 7 9 ft2
  • E 5 3 3 1 3 ft2

Q21:

How much fencing would a gardener need in order to place a fence around a square garden with an area of 324 square feet?

Q22:

If the ratio between the perimeters of two squares is 1 0 3 , what is the ratio between their areas?

  • A 5 1
  • B 1 2 5
  • C 2 0 3
  • D 1 0 0 9
  • E 5 3

Q23:

Find the area of a square whose side length is 1 1 1 𝑎 .

  • A 1 1 1 𝑎
  • B 1 1 2 1 𝑎
  • C 1 1 2 1
  • D 1 1 2 1 𝑎

Q24:

The square millimetre is the area of a square whose side length is .

  • Atwo millimetres
  • Bhalf of a millimetre
  • Cone square millimetre
  • Done millimetre

Q25:

Find the perimeter of a square whose area is 64 cm2.

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