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1. Solid Geometry – 1 (2D)

2. 1. Length of rectangle is increased by 25% and breadth is decreased by
20%. Find % change in area?
2. While cycling at a rate of 18kmph, A farmer is taking 10m covering the
boundary of his rectangular farm field. Find the cost of blowing the field
at a rate of 10/- per sq metre?
3. Length is increased successively by 20% and 25%. By what % the
breadth has to be decreased so that area is decreased by 20% ?
4. 4 horses are tethered at the 4 corners of a square field of side 7m. Find
area of the field untouched by the horses at the centre of field?
5. Area of square is increased by 125%. By what % the side is
increased if so ?

3.  Area = L B Diagonal (D) =
 Perimeter = 2(L + B)
 Area = Diagonal (D) = s
 Perimeter = 4s
 Area =
 Perimeter = 2
Perimeter – total length of the boundary
Volume – space occupied by a 3D shape
Capacity - space that a 3D shape can hold
L
B
Rectangle
r
Square
Circles
2 - DIMENSIONAL

4. a
c = base
b
h
 Area = =
 Perimeter = a + b + c s =
 Sector is a part of circle that makes certain angle
at the centre.
 Length ( ) =
 Area (A) =
 Perimeter (P) =
 Area =
 Perimeter = 4s
bisect each other at 90
s
Rhombus

5. h Area =
 Perimeter = 2 (
h
 Area =
Trapezium
Parallelogram

6. 1. Length of rectangle is increased by 25% and breadth is decreased by
20%. Find % change in area?
Method -1
25% i.e.
 Let initial value be
 Final values become 4
20
 Change in area = 0%
Ans :
Method -2
100 125 100
0% change
25% 20%

7. Side of a square is increased by 20% . Find % change in area?
Method -1
 Let initial value be
 Final values become 6
 Change in area = 11
Ans :
Method -2
100 120 144
44% change
20% 20%
% change =
36 −25
100
= 44%
% Change in area = 44%
100 % = 120
20% = 24
2.

8. Length is increased successively by 20% and 25%. By what % the
breadth has to be decreased so that area is decreased by 20% ?
Ans :
100 120 150 80
20% change in area
20% 25%
% change = 100
= %
% Change in breadth =
140
%
100 % = 120
20% = 24
?
3.

9. 4 horses are tethered at the 4 corners of a square field of side 7m. Find area
of the field untouched by the horses at the centre of field?
Ans :
Area of the field untouched by the horses at the centre of field = 10.535 sqm
4.
Can’t be determined because the length of the rope to which horses are
threatened is not given
If they are tethered in a manner such that they can just touch the other at their
max ridge = total square area – touched area
= 49 -
= 49 – 38.465
= 10.535 sqm

10. Area of square is increased by 125%. By what % the side is increased if so ?
Ans :
% change = 100
= 50%
% Increase in side = 50 %
s1 s2
10 10 15 15
5.

11. Subscribe to :
Continued…..
Problems for practice are given in the description of the video.

12. 1. Side of a square is increased by 20% . Find % change in area?
2. Radius of circle is increased by 10%. Find the % change in its
area?
3. Length of the rectangle is increased by 50%. By what % its
breadth has to be decreased to maintain the same area?
4. Length of the rectangle is increased by 25%. But its area is
decreased by 20%. If so by what % the breadth has to be
decreased?

13. Side of square is increased by 20%. By what % the area is changed?
Ans :
100 120 132
32% increase in area
20% 20%
% Increase in area= 32 %
4.

14. Radius of a circle is increased by 20%. By what % the area is changed?
Ans :
100 120 132
32% increase in area
20% 20%
% Increase in area= 32 %
2.

15. Length of the rectangle is increased by 50%. By what % the breadth
has to be decreased to maintain the same area?
Ans :
100 150 100
0% change in area
50% x%
x = 100
= %
% Change in breadth =
0
%
3.

16. Length of the rectangle is increased by 25%. But its area is
decreased by 20%. If so by what % the breadth has to be
decreased?
Ans :
100 125 80
20% change in area
25% x%
x = 100
= %
% Decrease in breadth = %
4.