Question

all formulas of mensuration of 8th

Answer 1

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 = 




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