Mensuration.

Triangle:

Perimeter of triangle = a+b+c.

1)Area of triangle = √(S(S-a)(S-b)(S-c))

Here, S = Semiperimeter=(a+b+c)⁄2 , a,b,c are sides of triangle

2)Area of triangle = ½bh.

Here b= base of ∆, h = height of ∆.

3)Area of equilateral ∆ = √3/4 a² = ½ ah.

Here, a= Side of ∆, h = height of ∆.

⇒h=√3⁄2 a.

4) Area of Right angled ∆ = ½ ab.

a, b are sides of ∆.

Then hypotenuse= √(a²+b²) .

5) area of Isosceles ∆ = ½ b× AD.

Where AD = √〈a²-(b²⁄4)〉 .

Quadrilateral:

1)perimeter of parallelogram = 2(a+b)

Area of parallelogram = bh

Polyhedron: Solid objects having flat surfaces

Prism : The polyhedron have top and base as same polygon and other faces are rectangular (parallelogram).

Pyramid : Polyhedron which have a polygon as base and a vertex rest of the faces are triangles.

Euler ‘s formula for polyhedron : E+2 = F+V.
here, E = Edges of polyhedron, F = Faces, V = Vertices.
LSA = Lateral surface area, TSA = Total surface area.

1. LSA of Prism = Perimeter of base × height
2. TSA of prism = LSA + 2( area of base)
3. Volume of prism = Area of base × height

Cube:

1. 1) LSA = 4a² (a = length of cube).
2. 2) TSA = 6a².
3. 3)Volume = a³.

Cuboid:

1. LSA = 2h(l+b)  (l= length,b= breadth,h=height).
2. TSA = 2(lb+bh+lh).
3. Volume = lbh.

Cylinder:

1. CSA OF CYLINDER = 2πrh  ( CSA=curved surface area)
2. TSA = 2πr(h+r)
3. Volume = πr²h  

PYRAMID:

1. LSA = ½ (Perimeter of base × slant height.)
2. TSA = LSA +Area of base.
3. Volume= 1⁄3 ( Area of base × height).

Cone:

1. CSA = πrl ( r = radius, l= slant height,h = height).
2. TSA = πr(l+r) .
3. Volume = 1⁄3 πr²h. 

In cone   l²=h²+r².

Sphere:

1. CSA  = TSA = 4πr².
2. Volume = 4/3   πr³.     (r= radius of sphere).

Hemi Sphere:

1. CSA = 2πr².
2. TSA = 3πr².
3. Volume = 2/3   πr³.