1. Square:figure
(1)Area = a^{2}Sq units.
(or)
(2)Perimeter = P =4a
(or)
(3)Digonal (or)length of the rod that can be placed=
2.Rectangle:figure
(1)Area =
(2)Perimeter = P =
(3)Digonal =
Þb = Öd^{2}l^{2} Þl = Öd^{2}b^{2}
3.If area of plot is given as 'z'm^{2} and the ratio of l:b is given as x:y, then length is
l = x * [Öz/(x*y)]
b = y * [Öz/(x*y)]

4.
length required=(length * breadth of a room)/width of the carpet 
5.
No:of stones =(length * breadth of a room)/(length * breadth of a stone) 
6.
A_{2}/A_{1}= (a_{2}/a_{1})^{2} = (d_{2}/d_{1})^{2} 
7.
8.Circle:figure
(1)Area =
(2)
(3)Perimeter (or) Circumference =
Where P = 22/7 (or) 3.14 (4)
A = c^{2}/(4 P) (or) c = Ö4 PA = 2ÖPA 
9. % dec in Area =
fs [(r_{1}^{2}  r_{2}^{2})/r_{1}^{2}] * 100 
10. Distance travelled in 'N' revolutions is,
D = N * Pd (or) N = D/(Pd) 
11.Area left ungrazed =
12.Road out of the garden:figure
(1)Area of the road =
2w[l+b+2w] = [(l+2w)(b+2w)](l*b) 
Road inside the garden:figure
(2)Area of the road =
Two parallel roads:figure
(3)Area of the road =
13.Traingles:
(1)Right angled traingles:figure
Area = (1/2)*b*h
(2)Equilateral traingles:figure
Area=
Perimeter = P =
Height=
(3)Scalene traingle:figure
Perimeter = P =
Þs=(a+b+c)/2
Area =
(4)Isosceles traingle:figure
Perimeter = P
Area =
14.Volumes: (a)Cube:figure
(1)Lateral surface area =
(2)Total surface area =
(3)Volume of a solid = Base area * Height =
(4)Diagonal (or) Longest pole = d =
(b)Cuboid:figure
(1)Lateral surface area = A_{L} =
(2)Total surface area = A_{T}
(3)Volume = V =
(4)Diagonal = d =
(5)No:of boxes =
(lbh)/l_{1}b_{1}h_{1} = (Volume of big box)/(Volume of small box) 
15.
a^{3} = v_{1}^{3}+v_{2}^{3}+v_{3}^{3} 
16.
a_{1}/a_{2} = (v_{1}/v_{2})^{1/3} 
17.No:of boxes(if areas are given) =
a^{3}/a_{1}^{3} = (a/a_{1})^{3} 
(18)Cylinder:figure
(1)Lateral surface area = A_{L} =
(2)Total surface area = A_{T}
(3)
(4)Volume = v =
(5)Area of each flat surface i.e of ends =
(19)Cone:figure
(1)Slant height = L =
(2)Volume of the cone =
(3)Curved surface area of cone =
(4)Total surface area =
(5)
v_{1}/v_{2}=(r_{1}/r_{2})^{2} * h_{1}/h_{2} 
20.
Hh = (4/3) * r_{s} ^{3}/r_{d}^{2} 
21.Area of circle inscribed in an equilateral traingle is r^{2}.It's height is,
(22)Sector:figure
(1)
(2)A =
(3)Circumference,c =
(23)Four circular carboard pieces,each of radius 'r'cm are placed in such a way that each piece touches two other pieces.The area of the space enclosed by four pieces is,
(24)Rhombus:figure
(1)
4a^{2} = d_{1}^{2} + d_{2}^{2} 
(2)Area =
(3)Perimeter = P =
(25)Parallelogram:figure
(1)Area of D^{le}ABC
(2)Area of D^{le}ACD
(3)Area of parallelogram =
(26)Trapezium:figure
(1)Area of Trapezium=Area of (D^{le}ABC + D^{le}ACD)
1/2(ah) + 1/2(bh) = [(1/2)h][a + b] 
(27)Sphere:figure
(1)Surface area =
(2)Volume =
(3)
A_{1}/A_{2} = (r_{1}/r_{2})^{2} 
(4)
v_{1}/v_{2} = (r_{1}/r_{2})^{3} 
(5)
v_{1}/v_{2} = (A_{1}/A_{2})^{3/2} 
(6)
A_{1}/A_{2} = (v_{1}/v_{2})^{2/3} 
28.Area of four walls =
2 * (length + breadth) * height 

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