formule of mathematics class 8 of mensuration
Answers
Step-by-step explanation:
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)
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