Square MCQ Quiz - Objective Question with Answer for Square - Download Free PDF
Last updated on Jul 3, 2025
Latest Square MCQ Objective Questions
Square Question 1:
The area of a square is 144 m². What is the perimeter of the square?
Answer (Detailed Solution Below)
Square Question 1 Detailed Solution
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
Square Question 2:
If the perimeter of a square is 32 cm, The area of another square is [ x +10] cm2 whose side is 2 times the earlier square. Find the side of square whose perimeter is x cm?
Answer (Detailed Solution Below)
Square Question 2 Detailed Solution
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.
Square Question 3:
If each side of a square be increased by 10%, the percentage increase in area is
Answer (Detailed Solution Below)
Square Question 3 Detailed Solution
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%
Square Question 4:
A square sheet of 10 cm sides is folded along its diagonal to form an isosceles right triangle, and then hypotenuses are folded successively two times to form isosceles right triangles. What is the length of each equal side after the third folding?
Answer (Detailed Solution Below)
Square Question 4 Detailed Solution
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
Square Question 5:
Perimeter of square is 64 m. Length of rectangle is 4 m more than the side of square. Breadth of rectangle is 12 m. Find the area of rectangle?
Answer (Detailed Solution Below)
Square Question 5 Detailed Solution
Calculation
First, side of square:
Side = 64/4 = 16 m
Length of rectangle = 16 + 4 = 20
Area of rectangle = Length × Breadth = 20 × 12 = 240
Top Square MCQ Objective Questions
The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
Answer (Detailed Solution Below)
Square Question 6 Detailed Solution
Download Solution PDFGiven:
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
Answer (Detailed Solution Below)
Square Question 7 Detailed Solution
Download Solution PDFGiven:
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.
A square park having a side 20 m has two roads each 2 m wide running in the middle of it and parallel to its length and breath. What will be cost of gravelling the path at the rate of Rs. 100/m2?
Answer (Detailed Solution Below)
Square Question 8 Detailed Solution
Download Solution PDFGiven:
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
Calculate the length of the diagonal of a square if the area of the square is 32 cm2.
Answer (Detailed Solution Below)
Square Question 9 Detailed Solution
Download Solution PDFGiven:
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
∴ Length of the diagonals are 8 cm.Calculate the length of the diagonal of a square if the area of the square is 50 cm2.
Answer (Detailed Solution Below)
Square Question 10 Detailed Solution
Download Solution PDFGiven:
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
Thus, length of diagonal of square = √2a = √2 × 5√2 = 10 cmIf the side of a square increases by 20%, then what will be a percent increase in its perimeter?
Answer (Detailed Solution Below)
Square Question 11 Detailed Solution
Download Solution PDFGiven:
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.
Total area of the piece of glass square is 1444 cm2. Which is placed above a square table. The width between the table and the edge of the glass piece is 9 cm. Tell the length of the table. (in cm)
Answer (Detailed Solution Below)
Square Question 12 Detailed Solution
Download Solution PDFGiven:
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.
A man walking at a speed of 3km/h crosses a square field diagonally in 5 minutes. What is the area of the field (in m2) ?
Answer (Detailed Solution Below)
Square Question 13 Detailed Solution
Download Solution PDFGiven:
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.
A wire when bent in the form of a square encloses an area of 484 sq. cm. If the same wire is bent in the form of a circle, what is the area enclosed by it?
Answer (Detailed Solution Below)
Square Question 14 Detailed Solution
Download Solution PDFArea 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.
The diagonal of the square is 8√2 cm. Find the diagonal of another square whose area is triple that of the first square.
Answer (Detailed Solution Below)
Square Question 15 Detailed Solution
Download Solution PDFConcept Used:
Diagonal of square = √2 a
Calculations:
Diagonal of square = √2 a
So, √2 a = 8√2
⇒ a = 8
⇒ a² = 64 cm²
So, the area if another square = 3(64) = 192
So, it's diagonal= √2 a = √2 × √192 = 8√6 cm
Hence, The Required value is 8√6 cm