Square MCQ Quiz - Objective Question with Answer for Square - Download Free PDF

Given:

Area of the square = 144 m²

Formula used:

Area of a square = Side × Side

Perimeter of a square = 4 × Side

Calculation:

Side = √(Area) = √144 = 12 m

Perimeter = 4 × Side = 4 × 12 = 48 m

∴ The perimeter of the square is: 48 m

Given:

Perimeter of square = 32 cm

Area of another square = x + 10 cm²

Side of another square = 2 × side of earlier square

Formula used:

Perimeter = 4 × side

Area = side²

Calculations:

⇒ side = 32 ÷ 4 = 8 cm

New side = 2 × 8 = 16 cm

Area = 16² = 256 cm²

x + 10 = 256 ⇒ x = 246

Now, x = 246 ⇒ Perimeter = 246 cm

Side = 246 ÷ 4 = 61.5 cm

∴ Side of square whose perimeter is x cm is 61.5 cm.

Given:

Side of a square increased = 10%

Formula used:

Increase = New number - Original number

% increase = (Increase/Original Number) × 100

Area of square = side2

Calculations:

Let the side of the square be a 

Area of a square with side a = a²

After increasing percentage of side a by 10% = a + 10% of a

⇒ a(1 + 10/100) = a(1 + 1/10)

⇒ a(11/10) = 11a/10

Area of the square after increasing side by a = (11a/10)²

⇒ (11a/10) × (11a/10) = 121a²/100

⇒ 1.21a²

Percentage change in area of square =[(1.21a² - a²)/a²] × 100

⇒ [a²(1.21 - 1)/a²] × 100 = 0.21 × 100 

⇒ 21%

∴ Percentage change in area of square is 21%

Alternate Method

Percentage increase in a regular polygon = x + y + (xy/100)

In square length and breadth are same, x = y

Percentage increase = x + x + (xx/100)

⇒ 2x + x²/100 = 2 × 10 + 10 × 10/100

⇒ 20 + 1 = 21%

∴ The required percentage is 21%

Given:

Initial square side = 10 cm

Each folding forms an isosceles right triangle from the hypotenuse of the previous triangle

Formula used:

In an isosceles right triangle, if the hypotenuse = h, then each equal side = \(\dfrac{h}{√{2}}\)

Calculations:

First fold: Hypotenuse = diagonal of square = \(√{10^2 + 10^2} = √{200} = 10√{2} \)

Equal side 1 = \(\dfrac{10√{2}}{√{2}} = 10\)

Second fold: Hypotenuse = 10

Equal side 2 = \(\dfrac{10}{√{2}} = \dfrac{10√{2}}{2} = 5√{2} \)

Third fold: Hypotenuse = 5 √2

Equal side 3 = \(\dfrac{5√{2}}{√{2}} = 5\)

The length of each equal side after the third folding is 5 cm

Calculation

First, side of square:

Side = 64/4 = 16 m

Length of rectangle = 16 + 4 = 20 

Area of rectangle = Length × Breadth = 20 × 12 = 240

Given:

The width of the path around a square field = 4.5 m

The area of the path = 105.75 m2

Formula used:

The perimeter of a square = 4 × Side

The area of a square = (Side)²

Calculation:

Let, each side of the field = x

Then, each side with the path = x + 4.5 + 4.5 = x + 9

So, (x + 9)² - x² = 105.75

⇒ x2 + 18x + 81 - x2 = 105.75

⇒ 18x + 81 = 105.75

⇒ 18x = 105.75 - 81 = 24.75

⇒ x = 24.75/18 = 11/8

∴ Each side of the square field = 11/8 m

The perimterer = 4 × (11/8) = 11/2 m

So, the total cost of fencing = (11/2) × 100 = Rs. 550

∴ The cost of fencing of the field is Rs. 550

Shortcut TrickIn such types of questions, 

Area of path outside the Square is, 

⇒ (2a + 2w)2w = 105.75

here, a is a side of a square and w is width of a square

⇒ (2a + 9)9 = 105.75

⇒ 2a + 9 = 11.75

⇒ 2a = 2.75

Perimeter of a square = 4a

⇒ 2 × 2a = 2 × 2.75 = 5.50

costing of fencing = 5.50 × 100 = 550

∴ The cost of fencing of the field is Rs. 550

Given:

Total cost of fencing = Rs. 10080

Cost of fencing per metre = Rs. 20

Concept used:

Perimeter = Total cost / Cost per metre

Area of the pavement = area of outer square - area of inner square.

Calculation:

According to the question,

Total cost of fencing = 10080

Perimeter of square = 10080/20 = 504 m

⇒ Side of square = 504/4 = 126 m

According to the diagram,

Breadth of the pavement = 2 × 3m = 6m

Side of inner square = 126 - 6 = 120m

Area of pavement = (126 × 126) - (120 × 120)

⇒ Area of pavement = 1476

Cost of pavement = 1476 × 50 = Rs. 73800.

∴ The cost of pavement is Rs. 73800.

Given:

Side of park = 20 m

Width of the road = 2 m

Rate of traveling the path = 100/m2

Figure:

Calculation:

Area of the road = area of rectangular path along length of square and breadth of square - common square area

⇒ 2 × (20 × 2) - 2 × 2 = 80 - 4 = 76 m²

∴ Cost of gravelling the path = 76 × 100 = Rs. 7,600

Given:

Area of square = 32 cm²

Formula Used:

Area = (side)²

Diagonal = √2 × side

Calculation:

Let, length of side of the square be x

According to the question,

⇒ x² = 32

⇒ x = √32

⇒ x = 4√2

Diagonal = 4√2 × √2 = 8 cm

Given:

Area of the square = 50 cm²

Formula used:

Area of square = a²

For square of side ‘a’, diagonal = √2a

Calculation:

a² = 50 cm²

⇒ a = √(5 × 5 × 2) = 5√2 cm

Given:

Let the side of the square be x

And Perimeter of square = 4x

Formula Used:

Perimeter of square = 4 × (side)

Area of Square = (side)²

Area of Circle = π × (radius)² 

Perimeter of Circle = 2 × π × (radius)

Concept :

If sides increase by 20%. So Perimeter also increases by 20%

Sides become 1.2 times original

So, Perimeter becomes 4 × 1.2 = 1.2 times original

Alternative solution:

Let the side of the square be 100 cm

Side of the square is increased by 20% becomes = 100 + 100 × 20/100

⇒ 120 cm

Perimeter before increase = 4 × 100 = 400 cm

After 20% increased = 4 × 120 = 480 cm

Increase in percentage = [(480 - 400)/400]× 100

⇒ 20%

Mistake PointsPlease attention there asks the Perimeter, not the area, mostly students mark the 44% suppose to the area, but ask the perimeter.

Given:

Area of the piece of glass square = 1444 cm2

The piece is placed above a square table.

Width between the table and the edge of the piece = 9 cm

Concept used:

If two rectangular sheets are placed on each other and the width between their edges = w, then

Length of the bigger sheet = Length of the smaller sheet + (2 × w)

Formula:

Side of a square = √(a²) 

Where, a² = Area of the square

Calculation:

According to the question,

Side of piece of glass square = √1444 = 38 cm

So, length of the table = 38 + (2 × 9) = 38 + 18 = 56 cm

∴ The length of the table is 56 cm.

Given:

Man walks 3 km/h

He takes 5 mins to cross the square field diagonally.

Concept used:

If A is the side of the measure of each side of a square, then A² is the area and A√2 is the measure of its diagonal.

Solution:

Man travels in 5 mins = 3 × (5/60) = 1/4 km = 250m

So, the length of the diagonal of the square field = 250m

Let the measure of each side of the square field be L.

According to the question,

L√2 = 250

⇒ L = 125√2

⇒ L² = 31250

∴ The area of the square field is 31250m².

Area of the square = 484 sq. cm

Let each side b x cm

x² = 484

⇒ x = √484 = 22 cm

∴ Length of the wire = 4 × 22 = 88 cm

∴ Circumference of the desired circle = 88 cm

⇒ 2 × (22/7) × radius = 88

⇒ radius = 14 cm

∴ Area = πr² = (22/7) × 14 × 14 = 616 sq. cm

Smart Trick

Here, area of circle is a multiple of π and radius of the circle. Hence, answer must be a multiple of 11 and 7.

In all given options, we find 616 is the only option that is divisible by 7 and 11 both.

∴ Option 2 is the correct answer.

Concept Used:

Diagonal of square = √2 a

Calculations:

Diagonal of square = √2 a