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 |
Discuss it
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 |
Discuss it
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.
100 m | |
183√3 m | |
180√3 m | |
200 m |
Discuss it
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?
46√2 sq . m | |
441 sq. m | |
529 sq. m | |
1058 sq. m |
Discuss it
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 |
Discuss it
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 |
Discuss it
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 |
Discuss it
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 |
Discuss it
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:
500 m | |
400 m | |
300 m | |
200 m |
Discuss it
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 |
Discuss it
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%