# 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? 169 sq. m 200 sq. m 275 sq. m 400 sq. m

Question 1-Explanation:

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? 7/2 sq. m 5 sq. m 6 sq. m 11 sq. m

Question 2-Explanation:

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. 100 m 183√3 m 180√3 m 200 m

Question 3-Explanation:

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? 46√2 sq . m 441 sq. m 529 sq. m 1058 sq. m

Question 4-Explanation:

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: 30√3 4*√216 4*√218 None of the above

Question 5-Explanation:

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? 136 140 180 192

Question 6-Explanation:

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. 11 15 21 60

Question 7-Explanation:

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? 24/7 40/7 11 14

Question 8-Explanation:

A = πr

r = √A/π = √616 / π

14

 Question 9

The perimeter of a field of length 100 m and breadth is 50 m is: 500 m 400 m 300 m 200 m

Question 9-Explanation:

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? 13.58 14.97 15.26 22.75

Question 10-Explanation:

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%

There are 16 questions to complete.

• Last Updated : 27 Sep, 2023