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Mensuration Formulas

**Mensuration** is the branch of mathematics which deals with the study of Geometric shapes, their area, volume and related parameters.

Some important **mensuration formulas** are:

1. Area of rectangle (A) = length(l) × Breath(b)

2. Perimeter of a rectangle (P) = 2 × (Length(l) + Breath(b))

3. Area of a square (A) = Length (l) × Length (l)

4. Perimeter of a square (P) = 4 × Length (l)

5. Area of a parallelogram(A) = Length(l) × Height(h)

6. Perimeter of a parallelogram (P) = 2 × (length(l) + Breadth(b))

7. Area of a triangle (A) = (Base(b) × Height(b)) / 2

And for a triangle with sides measuring “a” , “b” and “c” , Perimeter = a+b+c

and s = semi perimeter = perimeter / 2 = (a+b+c)/2

And also: Area of triangle =

This formulas is also knows as “Heron’s formula”.

8. Area of triangle(A) =

Where A, B and C are the vertex and angle A , B , C are respective angles of triangles and a , b , c are the respective opposite sides of the angles as shown in figure below:

area of triangle - mensuration

9. Area of isosceles triangle =

Where a = length of two equal side , b= length of base of isosceles triangle.

10. Area of trapezium (A) =

Where “a” and “b” are the length of parallel sides and “h” is the perpendicular distance between “a” and “b” .

11. Perimeter of a trapezium (P) = sum of all sides

12. Area of rhombus (A) = Product of diagonals / 2

13. Perimeter of a rhombus (P) = 4 × l

where l = length of a side

14. Area of quadrilateral (A) = 1/2 × Diagonal × (Sum of offsets)

15. Area of a Kite (A) = 1/2 × product of it’s diagonals

16. Perimeter of a Kite (A) = 2 × Sum on non-adjacent sides

17. Area of a Circle (A) =

Where r = radius of the circle and d = diameter of the circle.

18. Circumference of a Circle =

r= radius of circle

d= diameter of circle

19. Total surface area of cuboid =

where l= length , b=breadth , h=height

20. Total surface area of cuboid =

where l= length

21. length of diagonal of cuboid =

22. length of diagonal of cube =

23. Volume of cuboid = l × b × h

24. Volume of cube = l × l × l

25. Area of base of a cone =

26. Curved surface area of a cone = C =

Where r = radius of base , l = slanting height of cone

27. Total surface area of a cone =

28. Volume of right circular cone =

Where r = radius of base of cone , h= height of the cone (perpendicular to base)

29. Surface area of triangular prism = (P × height) + (2 × area of triangle)

Where p = perimeter of base

30. Surface area of polygonal prism = (Perimeter of base × height ) + (Area of polygonal base × 2)

31. Lateral surface area of prism = Perimeter of base × height

32. Volume of Triangular prism = Area of the triangular base × height

33. Curved surface area of a cylinder =

Where r = radius of base, h = height of cylinder

34. Total surface area of a cylinder =

35. Volume of a cylinder =

36. Surface area of sphere =

where r= radius of sphere, d= diameter of sphere

37. Volume of a sphere =

38. Volume of hollow cylinder =

where , R = radius of cylinder , r= radius of hollow , h = height of cylinder

39. Right Square Pyramid:

If a = length of base , b= length of equal side ; of the isosceles triangle forming the slanting face , as shown in figure:

net diagram of right square pyramid

39.a Surface area of a right square pyramid =

39.b Volume of a right square pyramid =

40. Square Pyramid:

40.a. Johnson Pyramid:

- net diagram of johnson pyramid

Volume =

Total Surface Area:

40.b. Normal Square pyramid:

If a = length of square base and h = height of the pyramid then:

Volume =

Total Surface Area =

41. Area of a regular hexagon =

42. area of equilateral triangle =

43. Curved surface area of a Frustums =

44. Total surface area of a Frustums =

45. Curved surface area of a Hemisphere =

46. Total surface area of a Hemisphere =

47. Volume of a Hemisphere =

48. Area of sector of a circle =

where

= measure of angle of the sector , r= radius of the sector