Area and Volumes

Area of a rectangle = Length x Breadth

(Diagonal)² = (Length)² + (Breadth)²

Area of a square = (side)² = (½) (Diagonal)²

Area of 4 walls of a room = 2 (Length + Breadth) x Height

Area of a parallelogram = (Base x Height)

Area of a rhombus = (½) (product of diagonals)
When d₁ and d₂ are the two diagonals then side of rhombus
= (½) √d₁² + d₂²

Area of an equilateral triangle = (√3/4) (side)²

If a, b, c are the lengths of the sides of a triangle and
S = (½) (a + b + c), then :
Area of the triangle = √s(s-a) (s-b) (s-c)

Area of a triangle = (½) x Base x Height

Area of a trapezium = (½) (sum of parallel sides x distance between them)

Circumference of a circle = 2 л r

Area of a circle = л r²

Arc AB = (2 л r Ө)/360^o , where angle AOB = Ө and O is the centre

Area of sector AOB = (л r² Ө)/360^o

Area of sector AOB = (½) (arc AB) r

Cuboid : Let length = l, breadth = b and height = h units
volume of cuboid = (lbh) cubic units
whole surface of cuboid = 2 (lb + bh + lh) sq. units
diagonal of cuboid = √l² + b² + h² units

Cube : Let each edge (or side) of a cube be a units. Then :
volume of the cube = a³ cubic units
whole surface of the cube = (6a²) sq. units
diagonal of the cube = (√3a) units

Cylinder : Let the radius of the base of a cylinder be r units and its height (or length) be h units. Then :
volume of the cylinder = (л r² h) cu. units
curved surface area of the cylinder = (2 лrh) sq. units
total surface area of the cylinder = (2 л rh + 2 л r²) sq. units

Sphere : Le the radius of a sphere be r units. Then :
volume of the sphere = (4/3) л r³ cu. units
surface area of the sphere = (4 л r²) sq. units
volume of a hemisphere = (2/3) л r³ cu. units
curved surface area of the hemisphere = (2 л r²) sq. units
whole surface area of the hemisphere = (3 л r²) sq. units

Cone : Let r be the radius of the base, h the height and l the slant height of a cone. Then :
slant height l = √h² + r²
volume of the cone = (1/3) л r² h cu. units
curved surface area of the cone = (лrl) sq. units = (л r √r² + h²) sq. units
total surface area of the cone = (л rl + л r²)