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)/360o, where angle AOB = Ө and O is the centre

Area of sector AOB = (л r2 Ө)/360o

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)