Question

Maths formulae for in integer, rational number mensuration

Answer 1

Rectangle :

Area = lb
Perimeter = 2(l+b)

Square :

Area = a×a
Perimeter = 4a

Parallelogram

Area = l × h
Perimeter = 2(l+b)

Triangle :

Area =b×h/2 or √s(s-a)(s-b)(s-c)…………….where s=a+b+c/2

Right angle Triangle :

Area =1/2(bh)
Perimeter = b+h+d

Isosceles right angle triangle :

Area = ½. a2
Perimeter = 2a+d……………………….where d=a√2

Equilateral Triangle :

Area = √3. a2/4 or ½(ah)….where h = √3/2
Perimeter = 3a

Trapezium :

Area = 1/2h(a+b)
Perimeter = Sum of all sides

Rhombus :

Area = d1 × d2/2
Perimeter = 4l

Quadrilateral

Area =1/2 × Diagonal × (Sum of offsets)

Kite :

Area = d1×d2/2
Perimeter = 2 × Sum on non-adjacent sides

Circle :

Area = πr^2 or πd^2/4
Circumference = 2πr or πd
Area of sector of a circle = (θπr^2 )/360

Frustum :

Curved surface area = πh(r1+r2)
Surface area = π( r12+ h(r1+r2) + r22)

Cube :

Volume: V = l3
Lateral surface area = 4a2
Surface Area: S = 6s2
Diagonal (d) = √3l

Cuboid :

Volume of cuboid: lbh
Total surface area = 2 (lb + bh + hl) or 6l2
Length of diagonal =√(l^2+b^2+h^2)

Right Circular Cylinder :

Volume of Cylinder = π r2 h
Lateral Surface Area (LSA or CSA) = 2π r h
Total Surface Area = TSA = 2 π r (r + h)
Volume of hollow cylinder = π r h(R2 – r2)

Right Circular cone :

Volume = 1/3 π r2h
Curved surface area: CSA= π r l
Total surface area = TSA = πr(r + l )

Sphere

Volume: V = 4/3 πr3
Surface Area: S = 4πr2

Hemisphere :

Volume = 2/3 π r3
Curved surface area(CSA) = 2 π r2
Total surface area = TSA = 3 π r2

Prism :

Volume = Base area x h
Lateral Surface area = perimeter of the base x h

Pyramid:

Volume of a right pyramid = (1/3) × area of the base × height.
Area of the lateral faces of a right pyramid = (1/2) × perimeter of the base x slant height.
Area of whole surface of a right pyramid = area of the lateral faces + area of the base.

Tetrahedron :

Area of its slant sides = 3a2√3/4
Area of its whole surface = √3a2
Volume of the tetrahedron = (√2/12) a 3

Regular Hexagon :

Area = 3√3 a2 / 2
Perimeter = 6a

Some other Formula :

Area of Pathway running across the middle of a rectangle = w(l+b-w)
Perimeter of Pathway around a rectangle field = 2(l+b+4w)
Area of Pathway around a rectangle field =2w(l+b+2w)
Perimeter of Pathway inside a rectangle field =2(l+b-4w)
Area of Pathway inside a rectangle field =2w(l+b-2w)
Area of four walls = 2h(l+b)

Answer 2

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