MENSURATION FORMULAS

This page mensuration formulas is containing lots of math formulas of math in the topic mensuration.

Circle:

Area of circle = Π r ²

Circumference of circle = 2 Π r

Example problems of area of circle

Example problems of circumference of circle


Semi circle

Area of Semi circle= (1/2) Π r²

Perimeter of semi-circle = Πr

Example problems on semi circle


Quadrant


Area of quadrant = (1/4) Π r²

Example problems on quadrant


Equilateral triangle


Area of Equilateral-triangle = (√3/4) a²

Perimeter of Equilateral-triangle = 3a

Example problems on equilateral triangle


Scalene Triangle

Area of scalene triangle = √s(s-a)(s-b)(s-c)

Perimeter of scalene triangle

= a + b +  c

Example problems on scalene triangle


Square

Area of square = a²

Perimeter of square = 4a

Examples problems on area of square

Examples problems on perimeter of square


Rectangle

Area of rectangle = L x W

Perimeter of rectangle=2(l+w)

Examples problems on area of rectangle

Examples of perimeter of rectangle

Quadrilateral


Area of quadrilateral

=(1/2) x d x (h₁+h₂)

Example problems of area of quadrilateral

parallelogram

Area of parallelogram = b x h

Example problems of area of parallelogram

Example problems of perimeter of parallelogram


Rhombus


Area of rhombus =(1/2) x (d₁ x d₂)

Examples problems on area of rhombus

Examples problems on perimeter of rhombus

Trapezoid


Area of trapezoid =(1/2) (a + b) x h

Examples problems on area of trapezoid

Sector

Area of the sector = (θ/360) x Π r ² square units

(or)  Area of the sector = (1/2) x l r square units   

Length of arc = (θ/360) x 2Πr

Examples problems on area of sector

Examples problems on length of arc

Worksheet for length of arc

Perimeter of sector worksheets

Area of sector worksheet

Cylinder

Curved surface area = 2 Π r h

Total surface area = 2 Π r (h + r)

Volume = Π r² h

r-radius , h - height

Examples problems of cylinder


Hollow cylinder:

Curved surface area= 2Π h (R+r)

Total surface area =  2 Π (R + r) (R - r + h)

Volume = Π h (R² - r²)

Curved surface area practice Worksheets1

Curved surface area practice Worksheets2


Cone

Curved Surface area = Π r L

Total surface area = Π r (L + r)

Volume = (1/3) Π r²h

L² = r² + h²

Examples of cone


Sphere

Curved Surface area = 4 Π r²

Volume = (4/3) Π r³

Curved Surface area of hemisphere = 2 Π r²

Total Surface area of hemisphere = 3Πr²

Volume = (2/3) Π r³

Example problems of sphere


Hollow hemisphere:

Curved Surface area = 2 Π (R² + r²)

Total Surface area = Π (3 R² + r²)

Volume = (2/3) Π (R³ - r³)

Example problems of hemisphere


Frustum Cone

Volume of frustum cone

                   = (1/3) Π h (R²+r² + R r)

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