Mensuration 2D

  • Last Updated : 26 Dec, 2018

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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

Mensuration 2D    
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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?

A

7/2 sq. m

B

5 sq. m

C

6 sq. m

D

11 sq. m

Mensuration 2D    
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Question 2 Explanation: 

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

Question 3

Given: The area of a rectangle field is 2700 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

Mensuration 2D    
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Question 3 Explanation: 

5x * 4x = 2700
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

Mensuration 2D    
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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:

A

30√3

B

4*216

C

4*√218

D

None of the above

Mensuration 2D    
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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?

A

136

B

140

C

180

D

192

Mensuration 2D    
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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.

A

11

B

15

C

21

D

60

Mensuration 2D    
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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?

A

24/7

B

40/7

C

11

D

14

Mensuration 2D    
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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:

A

500 m

B

400 m

C

300 m

D

200 m

Mensuration 2D    
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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?

A

13.58

B

14.97

C

15.26

D

22.75

Mensuration 2D    
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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.
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