Maths Formulas for mensuration

Maths Formulas for mensuration

AREA & PERIMETER :

Shape Area Perimeter

* Circle ∏ (Radius)2 2∏(Radius)
* Square (side)2 4(side)
* Rectangle length*breadth 2(length+breadth)
* Area of a triangle = 1/2*Base*Height or
* Area of a triangle = √ (s(s-(s-b)(s-c)) where
a,b,c are the lengths of the sides and s = (a+b +c)/2
* Area of a parallelogram = Base * Height
* Area of a rhombus = 1/2(Product of diagonals)
* Area of a trapezium = 1/2(Sum of parallel sides)
(distance between the parallel sides)
* Area of a quadrilateral = 1/2(diagonal)(Sum of
sides)
* Area of a regular hexagon = 6(√3/4)(side)2
* Area of a ring = ∏(R2-r2) where R and r are the
outer and inner radii of the ring.
* Area of a circle=πr^2 or πd^2/4
* Area of semi-circle=πr^2/2
* Area of a quadrant of a circle=πr^2/4
* Area enclosed by two concentric circles=π(R^2-r ^2)
* Area of a sector=Ɵ/180 degree *πr

No of revolutions completed by a rotating wheel
in 1 minute=distance moved in 1 minute/
circumference

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# VOLUME & SURFACE AREA :

* Cube :
Let a be the length of each edge. Then,
Volume of the cube = a3 cubic units
Surface Area = 6a2 square units
Diagonal = √ 3 a units

* Cuboid :
Let l be the length, b be the breadth and h be
the height of a cuboid. Then
Volume = lbh cu units
Surface Area = 2(lb+bh+lh) sq units
Diagonal = √ (l2+b2+h2)

* Cylinder :
Let radius of the base be r and height of the
cylinder be h. Then,
Volume = ∏r2h cu units
Curved Surface Area = 2∏rh sq units
Total Surface Area = 2∏rh + 2∏r2 sq units

* Cone :
Let r be the radius of base, h be the height, and l
be the slant height of the cone. Then,
l2 = h2 + r2
Volume = 1/3(∏r2h) cu units
Curved Surface Area = ∏rl sq units
Total Surface Area = ∏rl + ∏r2 sq units

* Sphere :
Let r be the radius of the sphere. Then,
Volume = (4/3)∏r3 cu units
Surface Area = 4∏r2 sq units

* Hemi-sphere :
Let r be the radius of the hemi-sphere. Then,
Volume = (2/3)∏r3 cu units
Curved Surface Area = 2∏r2 sq units
Total Surface Area = 3∏r2 sq units

* Prism :
Volume = (Area of base)(Height)