Mensuration is the branch of Mathematics which deals with the study of geometric shapes, their area, volume and different parameters in geometric objects.

Rectangle

1. Area of rectangle = length(l) * Breath(b) = l x b

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

Square

3. Area of a square = Length (l) * Length (l) = l x l

4. Perimeter of a square = 4 * Length (l) = 4 x l

Parallelogram

5. Area of a parallelogram = Length(l) * Height(h) = l x h

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

Triangle

7. Area of a triangle = (Base(b) * Height(b)) / 2 = ½ x b x h

Perimeter = (a + b + c)

Area of triangle = √{s(s-a)(s-b)(s-c)} [Hero’s formula]

8. Area of triangle = ½ab∠C = ½bc∠A = ½ac∠B

9. Area of isosceles triangle = (b/4) * √(4a2-b2)

Trapezium

10. Area of trapezium = ½(a+b)h

11. Perimeter of a trapezium = sum of all sides

Rhombus

12. Area of rhombus =  Product of diagonals / 2

13. Perimeter of a rhombus = 4 * length

14. Area of quadrilateral = ½ * Diagonal * (Sum of offsets)

Kite

15. Area of a Kite = ½ * product of its diagonals

16. Perimeter of a Kite = 2 * Sum on non-adjacent sides

Circle

17. Area of a Circle = πr2 = πd2/4

18. Circumference of a Circle = 2πr = πd

Cube and Cuboid

19. Total surface area of cuboid = 2(lb + bh + lh)

20. Total surface area of cube = 6 * l2

21. Length of diagonal of cuboid = √(l2+b2+h2)

22. Length of diagonal of cube = √(3l)

23. Volume of cuboid = l * b * h

24. Volume of cube = l * l * l

Cone

25. Area of base of a cone = πr2

26. Curved surface area of a cone = C = πrl

27. Total surface area of a cone = πr(r+l)

28. Volume of right circular cone = (1/3) * πr2h

Prism

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

30. Surface area of polygonal prism = (Perimeter of base * height) + (Polygonal base area * 2)

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

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

Cylinder

33. Curved surface area of a cylinder = 2πrh

34. Total surface area of a cylinder = 2πr(r+h)

35. Volume of a cylinder = πr2h

Sphere

36. Surface area of sphere = 4πr2 = πd2

37. Volume of a sphere = (4/3) * πr3 = 1/6 * πd3

Other Figures

38. Volume of hollow cylinder = πrh(R2-r2)

39. Surface area of a right square pyramid = a √(4b2 - a2)

40. Volume of a right square pyramid = (1/3) * b2h

41. Area of a regular hexagon = 3√3a2)/2

42. Area of equilateral triangle = (√3/4) * a2

43. Curved surface area of a Frustums = πh(r1 + r2)

44. Total surface area of a Frustums = π (r12 + h(r1+r2) + r22)

45. Curved surface area of a Hemisphere = 2πr2

46. Total surface area of a Hemisphere = 3πr2

47. Volume of a Hemisphere = (2/3) * πr3 = (1/12) * πd3

48. Area of sector of a circle = (θr2π)/360