Mensuration 2D

Question 1

Jack went to the garden for a picnic. He saw a board in the garden with the area of the square garden mentioned as 625 sq.m. He is curious to know what will be the area of a path of width 2.5 m around it if the path is outside the garden?

• A. 169 sq. m
• B. 200 sq. m
• C. 275 sq. m
• D. 400 sq. m

Answer: (C)

area of the square garden=625m²
therefore side²=625m²
side=√625

side=25m
hence, the length of the side of the square garden is 25m.
therefore the length of the path=25+2.5+2.5
=25+5
=30m
total area along with the road=30×30
=900m²
hence, area of the path=900-625
=275 sq m

Question 2

Johnny went to an exhibition, he saw a triangular swing there. He noted the dimensions of the swing as 3m, 4m, and 5m. Find its area?

• A. 7/2 sq. m
• B. 5 sq. m
• C. 6 sq. m
• D. 11 sq. m

Answer: (C)

given is a right angled triangle 
½ * 3* 4 = 6 m2

Question 3

Given: The area of a rectangle field is 6000 sq.m. The ratio of the sides is 5:4, find the perimeter of the rectangular field.

• A. 100 m
• B. 183√3 m
• C. 180√3 m
• D. 200 m

Answer: (C)

5x * 4x = 6000
x2 = 300
x= 10√3
perimeter = (50√3)*2+(40√3)*2 = 180√3

Question 4

If the diagonal of a square has a length of 23√2. Find the area of the square?

• A. 46√2 sq . m
• B. 441 sq. m
• C. 529 sq. m
• D. 1058 sq. m

Answer: (C)

2a² = 2*23² => a² = 23² = 529 sq. m

Question 5

Given: The diagonals of a rhombus are 26 cm and 14 cm. Find the length of its boundaries:

• A. 30√3
• B. 4*√216
• C. 4*√218
• D. None of the above

Answer: (C)

Given:

• Diagonals of a rhombus = 14 cm and 26 cm.

To Find:

• Find its Perimeter i.e. length of boundaries.

Solution:

• To find the perimeter of the rhombus we should find the length of its side as perimeter = 4a, where a is the length of one side of the rhombus.
• As diagonals of the rhombus are perpendicular, they bisect each other.
• So, 26 cm is considered as 13 cm = x and 14 cm is considered as 7 cm = y
• Side of the rhombus, a = √(13^2+7^2)
• a = √218 cm
• Perimeter, p = 4a = 4*√218 cm

Question 6

Given: The sides of a rectangular garden are 36 m x 64 m. Find the perimeter of a square garden which is having the same area as that of the rectangle?

• A. 136
• B. 140
• C. 180
• D. 192

Answer: (D)

area of square L2= 36 m x 64 m 
L = 6*8 = 48
Perimeter of square = 48*4 = 192 meters

Question 7

Jimin was calculating the area of a square. He made a mistake in measuring the side of square, the error of 10% excess is made in calculating the side of a square by him. Find the % error in its area.

• A. 11
• B. 15
• C. 21
• D. 60

Answer: (C)

Area of square = L2
=(1.1L)2 = 1.21 L2
=21 %

Question 8

If a circular swing in an exhibition has an area of 616 sq.m. Find the radius of the swing?

• A. 24/7
• B. 40/7
• C. 11
• D. 14

Answer: (D)

A = πr² 

r = √A/π = √616 / π

14

Question 9

The perimeter of a field of length 100 m and breadth is 50 m is:

• A. 500 m
• B. 400 m
• C. 300 m
• D. 200 m

Answer: (C)

Perimeter = 2 ( l + b )

=> 2 ( 100 + 50 )

=> 2 × 150

=> 300 m

Question 10

If the radius of a circle is increased by 7.36%, then by how the area will be increased?

• A. 13.58
• B. 14.97
• C. 15.26
• D. 22.75

Answer: (C)

New Area of the Circle = Pi * (R + 7.36% of R)^2 = Pi * (R + 0.0736R)^2 = Pi * (1.0736R)^2 = Pi * R^2 * (1.0736)^2. Therefore, percentage increase in Area = [ Pi * R^2 * (1.0736)^2 - Pi * R^2 ]/ (Pi * R^2) = 1.0736^2 - 1 = 0.15261696 = 15.26%