Question

All formulas for mensuration class 6

Answer 1

Some important mensuration formulas for class 6 are :

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

A = l \times b



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

P = 2 \times(l + b)



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

A = l \times l



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

P = 4 \times l



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

A = l \times h

Parallelogram



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

P = 2 \times (l + b)



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

A = \frac{1}{2} \times b \times h

Triangle

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 = A = \sqrt{s(s-a)(s-b)(s-c)}

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



8. Area of triangle(A) = \frac{1}{2} a \times b \times \angle C = \frac{1}{2} b \times c \times \angle A = \frac{1}{2} a \times c \times \angle B

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
area of triangle - mensuration



9. Area of isosceles triangle = \frac{b}{4}\sqrt{4a^2 - b^2}

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



10. Area of trapezium (A) = \frac{1}{2} (a+b) \times h

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

Trapezium



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)

quadrilateral



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) = \pi r^2 = \frac{\pi d^2}{4}

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



18. Circumference of a Circle = 2 \pi r = \pi d

r= radius of circle

d= diameter of circle



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

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



20. Total surface area of cuboid = 6 l^2

where l= length



21. length of diagonal of cuboid = \sqrt{l^2+b^2+h^2}



22. length of diagonal of cube = \sqrt{3 l}



23. Volume of cuboid = l × b × h



24. Volume of cube = l × l × l



25. Area of base of a cone = \pi r^2



26. Curved surface area of a cone = C = \pi \times r \times l

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



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



28. Volume of right circular cone = \frac{1}{3} \pi r^2 h

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 = 2 \pi r h

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



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



35. Volume of a cylinder = \pi r^2 h



36. Surface area of sphere = 4 \pi r^2 = \pi d^2

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



37. Volume of a sphere = \frac{4}{3} \pi r^3 = \frac{1}{6} \pi d^3



38. Volume of hollow cylinder = \pi r h(R^2-r^2)

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
net diagram of right square pyramid

39.a Surface area of a right square pyramid = a \sqrt{4b^2 - a^2}

39.b Volume of a right square pyramid = \frac{1}{2} \times base \, \, area \times height



40. Square Pyramid:

40.a. Johnson Pyramid:

net diagram of johnson pyramid
net diagram of johnson pyramid
Volume = (1+ \sqrt{3})\times a^2
Total Surface Area: \frac{\sqrt{2}}{6} \times a^3

40.b. Normal Square pyramid:

If a = length of square base and h = height of the pyramid then:
Volume = V=\frac{1}{3}a^2h
Total Surface Area = a^2+a\sqrt{a^2+(2h)^2}



41. Area of a regular hexagon = \frac{3\sqrt{3}a^2}{2}



42. area of equilateral triangle = \frac{\sqrt{3}}{4} a^2



43. Curved surface area of a Frustums = \pi h (r_1 + r_2)



44. Total surface area of a Frustums = \pi (r_1^2 + h(r_1+r_2) + r_2^2)



45. Curved surface area of a Hemisphere = 2 \pi r^2



46. Total surface area of a Hemisphere = 3 \pi r^2



47. Volume of a Hemisphere = \frac{2}{3} \pi r^3 = \frac{1}{12} \pi d^3



48. Area of sector of a circle = \frac{\theta r^2 \pi}{360}

where \theta = measure of angle of the sector , r= radius of the sector

Answer 2

All formulas for mensuration for class 6th are given below:

• The perimeter of rectangle = 2(l+b)
• Area of rectangle = l × b
• The perimeter of square = 4 × side
• Area of square = side × side
• Area of triangle = 1/2 × base × height
• Area of parallelogram = Base × height
• Area of trapezium = 1/2 × (sum of parallel sides) × height
• Circumference of circle = 2πr( the value of pie is 22/7 or 3.14)
• Area of circle = πr²

( All these formulas are sufficient for completing all your questions from the mensuration chapter.)