Formulas of Area, Volume & Surface Area
***Rectangle :-
a. Area of a rectangle = (length × breadth)
b. Perimeter of a rectangle = 2 (length + breadth)
***Square :-
a. Area of square = (side)2
b. Area of a square = ½ (diagonal)2
Area of 4 walls of a room
= 2 (length + breadth) × height
***Triangle :-
a. Area of a triangle = ½ × base × height
b. Area of a triangle = , where
s = ½ (a + b + c), and a, b, c are the sides of the triangle
c. Area of an equilateral triangle = / 4 × (side)2
d. Radius of incircle of an equilateral triangle of side a = a / 2
e. Radius of circumcircle of an equilateral triangle of side a = a /
***Parallelogram***Rhombus***Trapezium :-
a. Area of a parallelogram = Base × Height
b. Area of a rhombus = ½ × (Product of diagonals)
c. The halves of diagonals and a side of a rhombus form a right angled triangle with
side as the hypotenuse.
d. Area of trapezium = ½ × (sum of parallel sides) × (distance between them)
**Circle***Arc***Sector :-
where R is the radius of the circle:
a. Area of a circle = πR2
b. Circumference of a circle = 2πR
c. Length of an arc = Ө/360 × 2πR
d. Area of a sector = ½ (arc × R)
= Ө/360 × πR2
***Cuboid :-
Let length = l, breadth = b & height = h units Then,
a. Volume = (l × b × h) cu units
b. Surface Area = 2 (lb + bh + hl) sq. units
c. Diagonal = units
***Cube :-
Let each edge of a cube be of length a. Then,
a. Volume = a3 cu units
b. Surface Area = 6a2 sq. units
c. Diagonal = ( × a) units
***Cylinder :-
Let radius of base = r & height (or length) = h. Then,
a. Volume = (πr2h) cu. units
b. Curved Surface Area = (2πrh) sq. units
c. Total Surface Area = 2πr(r + h) sq. units
***Cone :-
Let radius of base = r & height = h. Then,
a. Slant height, l = units
b. Volume = (⅓ πr2h) cu. units
c. Curved Surface Area = (πrl) sq. units
d. Total Surface Area = πr(r + l) sq. units
***Sphere :-
Let the radius of the sphere be r. Then,
a. Volume = (4/3 πr3) cu. units
b. Surface Area = (4πr2) sq. units
***HemiSphere :-
Let the radius of the sphere be r. Then,
a. Volume = (2/3 πr3) cu. units
b. Curved Surface Area = (2πr2) sq. units
c. Total Surface Area = (3πr2) sq. units
a. Area of a rectangle = (length × breadth)
b. Perimeter of a rectangle = 2 (length + breadth)
***Square :-
a. Area of square = (side)2
b. Area of a square = ½ (diagonal)2
Area of 4 walls of a room
= 2 (length + breadth) × height
***Triangle :-
a. Area of a triangle = ½ × base × height
b. Area of a triangle = , where
s = ½ (a + b + c), and a, b, c are the sides of the triangle
c. Area of an equilateral triangle = / 4 × (side)2
d. Radius of incircle of an equilateral triangle of side a = a / 2
e. Radius of circumcircle of an equilateral triangle of side a = a /
***Parallelogram***Rhombus***Trapezium :-
a. Area of a parallelogram = Base × Height
b. Area of a rhombus = ½ × (Product of diagonals)
c. The halves of diagonals and a side of a rhombus form a right angled triangle with
side as the hypotenuse.
d. Area of trapezium = ½ × (sum of parallel sides) × (distance between them)
**Circle***Arc***Sector :-
where R is the radius of the circle:
a. Area of a circle = πR2
b. Circumference of a circle = 2πR
c. Length of an arc = Ө/360 × 2πR
d. Area of a sector = ½ (arc × R)
= Ө/360 × πR2
***Cuboid :-
Let length = l, breadth = b & height = h units Then,
a. Volume = (l × b × h) cu units
b. Surface Area = 2 (lb + bh + hl) sq. units
c. Diagonal = units
***Cube :-
Let each edge of a cube be of length a. Then,
a. Volume = a3 cu units
b. Surface Area = 6a2 sq. units
c. Diagonal = ( × a) units
***Cylinder :-
Let radius of base = r & height (or length) = h. Then,
a. Volume = (πr2h) cu. units
b. Curved Surface Area = (2πrh) sq. units
c. Total Surface Area = 2πr(r + h) sq. units
***Cone :-
Let radius of base = r & height = h. Then,
a. Slant height, l = units
b. Volume = (⅓ πr2h) cu. units
c. Curved Surface Area = (πrl) sq. units
d. Total Surface Area = πr(r + l) sq. units
***Sphere :-
Let the radius of the sphere be r. Then,
a. Volume = (4/3 πr3) cu. units
b. Surface Area = (4πr2) sq. units
***HemiSphere :-
Let the radius of the sphere be r. Then,
a. Volume = (2/3 πr3) cu. units
b. Curved Surface Area = (2πr2) sq. units
c. Total Surface Area = (3πr2) sq. units
