Mensuration Formulas

Page 1

Area Formulas 2D

Mensuration Formulas for RECTANGLE

Area = Length x Width

Perimeter = 2(Length + Width)

Length of the Diagonal = √(Length² + Width²)

Mensuration Formulas for PARALLELOGRAM

Area = Base x Height

Perimeter = 2(Length + Width)

Mensuration Formulas for TRIANGLE

Area = 1/2(Base x Height)

Scalene Triangle

Perimeter = a + b + c

Area = √s(s-a)(s-b)(s-c)

s = semi perimeter = perimeter/2

Isosceles Triangle

Area = b/4√4a²-b²

Equilateral Triangle

Area = 3/4 x a²

Mensuration Formulas for TRAPEZIUM

Area = 1/2 (sum of parallel sides) (distance between parallel sides)

Perimeter = sum of all sides

Mensuration Formulas for RHOMBUS]

* product = result of two numbers multiplied

Area = 1/2 (product of diagonals)

Perimeter = 4(Length)

Mensuration Formulas for CIRCLE

Area = πr² = (πd²)4

Circumference = 2πr = πd

Semicircle

Area = (πr²)/2

Perimeter = (πr + d)

Sector

Area = ø/360 (2πr²)

Perimeter = 2r + arc length

Arc Length

ø/360 (2πr)

Segment

Area = A of sector - A of triangle

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Volume Formulas 3D

Main Formula for Uniform Cross Section =

Area of Base x Height

Mensuration Formulas for CUBE

Volume = Length x Width x Perpendicular Height

Mensuration Formulas for CYLINDER

Volume = πr²h

πr² = base area

Volume of Hollow Cylinder = π(R²-r²)

R = outer radius

Mensuration Formulas for CONE

Volume = 1/3 (πr²)h

Mensuration Formulas for SPHERE

Volume = 4/3(πr³)

Volume of Hemisphere = 2/3(πr³)

Page 3

Surface Area Formulas

Surface Area Formula for CUBE

Total Surface Area = 6( Length²)

Surface Area Formula for CYLINDER

Total Surface Area = 2πr² + 2πrh

2πr² = two circle bases

2πrh = curved rectangle

Surface Area of Hollow Cylinder = 2π (R+r)(h+R-r)

r is inner radius, R is outer radius and h is height

Surface Area Formula for CONE

Total Surface Area = πr² + πrℓ

ℓ = slant height

ℓ = √² + h²

Surface Area of Open Conical Flask = πrℓ

Curved Surface Area

Surface Area Formula for SPHERE

Total Surface Area = 4πr²

Hemisphere

Total Surface Area of Hemisphere = 2πr²

Surface Area of Open Hemisphere = 2πr