Question

mensuration all formulas.

Answer 1

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Mensuration is one of the topics in Quants. Now a days questions coming from this chapter also. Here we are providing you Some important formulas which is used in mensuration which are useful in SSC, Railways and other exams.



Rectangle :

Area = lbPerimeter  = 2(l+b)

Square :

Area = a×aPerimeter = 4a

Parallelogram

Area = l × hPerimeter = 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. a2Perimeter = 2a+d……………………….where d=a√2

Equilateral Triangle :

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

Trapezium :

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

Rhombus :

Area = d1 × d2/2Perimeter = 4l

Quadrilateral

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

Kite :

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

Circle :

Area =  πr^2 or πd^2/4Circumference = 2πr  or πdArea 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 = l3Lateral surface area = 4a2Surface Area: S = 6s2Diagonal (d) = √3l

Cuboid :

Volume of cuboid: lbhTotal surface area = 2 (lb + bh + hl) or 6l2Length of diagonal =√(l^2+b^2+h^2)

Right Circular Cylinder :

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

Right Circular cone :

Volume = 1/3 π r2hCurved surface area: CSA=  π r lTotal surface area = TSA = πr(r + l )

Sphere

Volume: V = 4/3 πr3Surface Area: S = 4πr2

Hemisphere :

Volume = 2/3 π r3Curved surface area(CSA) = 2 π r2Total surface area = TSA = 3 π r2

Prism :

Volume = Base area x hLateral 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√3/4Area of its whole surface = √3a2 Volume of the tetrahedron = (√2/12) a 3

Regular Hexagon :

Area =  3√3 a2 / 2Perimeter  = 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)

Hope this helps.
@TopperA1

Answer 2

perimeter :-

square = 4s
rectangle = 2 ( l+b)

area:-

square = a×a
rectangle = lb
circle = 22/7×r ×r
trapezium = 1/2 h ( a+ b)
rhombus = 1/2 ×d1×d2
triangle =1/2 bh
TSA
cube= 6× l×l
cuboid = 2 ( lb+ bh+ hl)
cylinder = 2 ×22/7×r (r+h)

LSA
Cube = 4l×l
cuboid = 2h ( l+b)
cylinder = 2×22/7×rh