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