Mensuration

Area – Area is the quantity that expresses the extent of a region or shape of a two-dimensional figure.

Surface Area – Surface area is a measure of the total area that the surface of the object occupies

Perimeter – The distance around a two-dimensional figure is known as the perimeter.

Volume – Volume is the amount of three-dimensional space enclosed by a closed surface.

Mensuration Formulae:

Square:

Area of a square = s²

Also,

Area of a square = $\frac{1}{2}d^2$

Perimeter = 4s

Side = $\sqrt{area}$

Diagonal = $\sqrt{2a^2}$

where,

s is the side of the square,

d is the diagonal of a square.

Rectangle:

Area of a Rectangle = l x b

where,

l is length of the rectangle,

b is breadth of the rectangle.

Triangle

Area of a triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

where,

$s = \frac{a + b + c}{2}$

a, b and c are the lengths of each sides of the triangle.

Also,

Area of a triangle = $\frac{1}{2}bh$

where,

b is the length of base of the triangle

h is the length of perpendicular to the base of the triangle.

Equilateral Triangle

Area of an equilateral triangle = $\frac{\sqrt{3}}{4}s^2$

where,

s is the side of the triangle.

Rhombus:

Area of a rhombus = $\frac{1}{2}ab$

where,

a & b are lengths of the two diagonals of the rhombus.

Parallelogram:

Area of a parallelogram = bh

where,

b is the length of the base of the parallelogram,

h is the height of the perpendicular to the base of the parallelogram.

Trapezoid:

Area of a trapezoid = $\frac{(a+b)}{2}h$

where,

a & b are the length of the parallel sides of the trapezoid,

h is the distance between the parallels.

Circle:

Area of a circle = $\pi r^2$

where,

r is the radius of the circle.

Also,

d=2r.

where,

d is the diameter of the circle

r is the radius of the circle.

Cube:

Volume of a cube = a³

Surface area of a cube = 6a²

Diagonal of a cube = $\sqrt{3}a$

Perimeter of a cube = 12a

where,

a is the length of a side of a cube.

Cuboid:

Volume of a cuboid = lxbxh

Surface area of a cuboid = 2(lb+bh+hl)

Diagonal of a cuboid = $\sqrt{l^2+b^2+h^2}$

where,

l is the length of the cuboid,

b is the breadth of the cuboid

h is the height of the cuboid.

Cylinder:

Volume of a cylinder = $\pi r^2 h$

Curved surface area of a cylinder = 2πrh

Total surface area of a cylinder = 2πr(r+h)

where,

r is the radius of the circular base of the cylinder

h is the height of the cylinder.

Cone:

Volume of a cone = $\frac{1}{3}\pi r^2h$

Curved Surface area of a cone = πrl

Total Surface area of a cone = πrl + πr²

where,

l is the slant height & l² = h² + r²

r is the radius of the circular base,

h is the height of the cone.

Sphere:

Volume of a sphere = $\frac{4}{3}\pi r^3$

Total surface area of a sphere = 4πr²

where,

r is the radius of the sphere.

Hemisphere:

Volume of a hemisphere = $\frac{2}{3}\pi r^3$

Curved surface area of a hemisphere = 2πr²

Total surface area of a hemisphere = 3πr²

Height of the hemisphere = r

where,

r is the radius of the hemisphere.

Notes:

1 Litre = 1000 cm³

1 Kg = 1000 cm³

$\sqrt{3} = 1.732$

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Mensuration