Geometry Formulas

Geometry is a branch of mathematics that deals with shape, size, relative position of figures, and the properties of space. It emerges independently in number of early cultures as a practical way of dealing with lengths, area and volumes.

Geometry can be divided into two different types: Plane Geometry and Solid Geometry. The Plane Geometry deals with shapes such as circles, triangles, rectangles, square and more. Whereas, the Solid Geometry is concerned in calculating the length, perimeter, area and volume of various geometric figures and shapes. And are also used to calculate the arc length and radius etc.

The main concern of every student about this subject is the Geometry Formula. They are used to calculate the length, perimeter, area and volume of various geometric shapes and figures.  There are many geometric formulas, which are related to height, width, length, radius, perimeter, area, surface area or volume and much more.

Some geometric formula are rather complicated and few you might hardly ever seen them, however, there are some basic formulas which are used in our daily life to calculate the length, space and so on.

Here is a list of several most important geometry formulas that you use for solving various problems.

Basic Geometry Formulas

$Perimeter \; of \; a \; Square = P = 4a$

Where a = Length of the sides of a Square

$Perimeter \; of \; a \; Rectangle = P = 2(l+b)$

Where, l = Length ; b = Breadth

$Area \; of \; a \; Square = A = a^{2}$

Where a = Length of the sides of a Square

$Area \; of \; a \; Rectangle = A = l \times b$

Where, l = Length ; b = Breadth

$Area \; of \; a \; Triangle = A = \frac{b \times h}{2}$

Where, b = base of the triangle ; h = height of the triangle

$Area \; of \; a \; Trapezoid = A = \frac{(b_{1}+b_{2})h}{2}$

Where, $b_{1}$ & $b_{2}$ are the bases of the Trapezoid ; h = height of the Trapezoid

$Area \; of \; a \; Circle = A = \pi \times r^{2}$

$Circumference \; of \; a \; Circle = A = 2\pi r$

Where, r = Radius of the Circle

$Surface \; Area \; of \; a \; Cube = S = 6a^{2}$

Where, a = Length of the sides of a Cube

$Surface \; Area \; of \; a \; Cylinder = S = 2\pi rh$

$Volume \; of \; a \; Cylinder = V = \pi r^{2} h$

Where, r = Radius of the base of the Cylinder ; h = Height of the Cylinder

$Surface \; Area \; of \; a \; Cone = S = \pi r (r + \sqrt{h^{2}+r^{2}})$

$Volume \; of \; a \; Cone = V = \pi r^{2} h$

Where, r = Radius of the base of the Cone, h = Height of the Cone

$Surface \; Area \; of \; a \; Sphere = S = 4 \pi r^{2}$

$Volume \; of \; a \; Sphere = V = \frac{4}{3}\pi r^{3}$

Where, r = Radius of the Sphere


Practise This Question

Some statements about isomerism are given 

(I) n - propyl amine and isopropyl amine are position isomers 
(II)n - butyl amine, isobutyl amine are chain isomers 
(III)n - propyl amine and tri methyl amine are functional isomers 

(IV)di ethyl amine and n - propyl methyl amine are metamers The correct statements are