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 ∆.
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)〉 .
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.
- LSA of Prism = Perimeter of base × height
- TSA of prism = LSA + 2( area of base)
- Volume of prism = Area of base × height
- 1) LSA = 4a² (a = length of cube).
- 2) TSA = 6a².
- 3)Volume = a³.
- LSA = 2h(l+b) (l= length,b= breadth,h=height).
- TSA = 2(lb+bh+lh).
- Volume = lbh.
- CSA OF CYLINDER = 2πrh ( CSA=curved surface area)
- TSA = 2πr(h+r)
- Volume = πr²h
- LSA = ½ (Perimeter of base × slant height.)
- TSA = LSA +Area of base.
- Volume= 1⁄3 ( Area of base × height).
- CSA = πrl ( r = radius, l= slant height,h = height).
- TSA = πr(l+r) .
- Volume = 1⁄3 πr²h.
In cone l²=h²+r².
- CSA = TSA = 4πr².
- Volume = 4/3 πr³. (r= radius of sphere).
- CSA = 2πr².
- TSA = 3πr².
- Volume = 2/3 πr³.