## Formulas and facts related to Area of various geometric shapes:

- Sum of the angles triangles is\(180^o \)
- Sum of angles of a quadrilateral is \(360^o \)
- Pythagoras Theorem for Triangle,\(\left(Hypotenues\right)^2\;=\;\left(Base\right)^{2\;}+\left(Height\right)^2 \)
- Area of triangle=\(\frac12 \)*Base*Height
- Area of square=\(\left(Side\right)^2\;=\;\frac12\left(Diagonal\right)^2 \)
- Area of a rectangle=(Length*Breadth)
- Area of a triangle=\(\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)} \),where a,b,c are the sides of the triangle and s=\(\frac12\left(a+b+c\right)\)
- Area of a equilateral triangle=\(\frac{\sqrt3}4x\left(Side\right)^2 \)
- Radius of incircle of a equilateral triangle=\(\frac a{2\sqrt3} \)
- Radius of circumcircle of an equilateral triangle of side a=\(\frac a{\sqrt3} \)
- Area of a rhombus=\(\frac12\)*(Product of diagonal)
- Arae of a trapezium=\(\frac12 \)*(Sum of parellel sides)*(Distance between them)
- Area of a circle of radius R is \(\mathrm{πr}^2\)
- Circumferance of a circle with radius R is \(2\mathrm{πr} \)
- Length of an arc= \(\frac{2\mathrm{πR}}{360} \),where \( \) is the central angle

## Formulas related to Surface Area and Volume:

There are many geometric shapes like Cuboid, Cube, Cone, Cylinder, Sphere and Hemisphere. With reference to the volume and surface area many questions are asked in Bank PO, SSC, Railway and other competitive exam on basis of these geometric shapes. So we need to remember some formulas to solve these types of problems. So these formulas are given below inside a box.

#### CUBOID

Let length = l, breadth = b, height = h.

Volume

=(l*b*h) cubic unitsSurface Area

=2(lb+bh+lh) sq.unitDiagonal

=\( \sqrt{l^2+b^2+h^2}\)units

#### CUBE

Let each edge of a cube be of length a.

Volume =\(a^3 \) cubic unitSurface Area

=6 \(a^2 \) sq.unitDiagonal

= \(\sqrt3a \) units

#### CYLINDER

Let radius of base = r and Height = h

Volume

=\( \left(\mathrm{πr}^2\mathrm h\right)\)cubic unitCurved Surface Area

=\(\left(2\mathrm{πrh}\right) \)sq.unitsTotal Surface Area

=\( \left(2\mathrm{πrh}+2\mathrm{πr}^2\right)\)sq.units

#### SPHERE

Let the radius of the sphere be r. Then,

Volume=\(\left(\frac43\mathrm{πr}^3\right)\)cubic units

Surface Area=\( \left(4\mathrm{πr}^2\right)\)sq.units

#### HEMISPHERE

Let the radius of a hemisphere be r. Then,

volume=\(\left(\frac23\mathrm{πr}^3\right)\)cubic units

Curved Surface area=\( \left(2\mathrm{πr}^2\right)\)sq.units

Total Surface Area =\( \left(3\mathrm{πr}^2\right)\)sq.units

1 liter=1000cm3

#### CONE

Let radius of base = r and height = h. Then,

Slant height=l=\( \sqrt{h^2+r^2}\) Volume

=\(\left(\frac13\mathrm{πr}^2\mathrm h\right) \) cubic units.Curved surface

=\(\left(\mathrm{πrl}\right) \)

=\(\left(\mathrm{πrl}+\mathrm{πr}^2\right) \)sq.units

\( \)