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# Mathematical Formulars For College Students

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A Succinct description of over 20 Formulars on Goemetric. Formulars that capture the Area of Cones to Surface Area of Rhombus.

## Content

Mathematical
Formulas
For College
Students

GEOMETRIC
Shapes and Solids

1. SQUARE
Where π is the Side and π the Diagonal
Where π© perpendicular distance to it from opp. vertices
ο· Normal
π΄ππΈπ΄ = 2(π₯ + π) × π‘
1 2
π΄ππΈπ΄ = π³ = π«
2
2

ππΈππΌππΈππΈπ = ππ³2 = 2π«2

1
2

2. RECTANGLE
Where π₯ is the lenght, π the breadth, and π‘ is height

ο· Normal Rectangle
π΄ππΈπ΄ = π₯ × π
ππΈππΌππΈππΈπ = 2(π₯ + π)
ο· 4 Walls of a Room
π΄ππΈπ΄ = 2(π₯ + π) × π‘

3. TRIANGLE
ο· Normal Triangle
Where π is the base and π‘ the height ,
π, π, π are the sides of the triangle,
π¬ is the semi − perimeter of the triangle.
1
π΄ππΈπ΄ = ππ‘ =
2

π¬ π¬ − π π¬ − π (π¬ − π)

ππΈππΌππΈππΈπ = π + π + π = 2π
ο· Isoceles Triangle
π
π΄ππΈπ΄ =
πππ − π π
4
ππΈππΌππΈππΈπ = 2π + π
1
π»πππππ‘ (π) =
πππ − π π
2

4. POLYGON
ο· Regular
π΄πππ ππ π»ππ₯ππππ =

3 3 ÷ 2 × (π ππππ )2

π΄πππ ππ πππ‘ππππ = [2

2 + 1] × (π ππππ )2

5. PARALLELOGRAM
Where π is the base and π slant ′diagonal′;
π‘ is the corresponding attitude.

π΄ππΈπ΄ = ππ‘
ππΈππΌππΈππΈπ = ππ + ππ

6. CIRCLE
Where π« is the radius, π is diameter,
π is the circumference of the circle.

2
2
π
π
1
2
π΄ππΈπ΄ = ππ« = π
=
= (π × π«)
4
4π
2

ππΈππΌππΈππΈπ = 2ππ« = Circumference of Circle

7. CIRCULAR SECTOR
Where π« is the radius, π is the length of the sector.
π΄ππΈπ΄ = ππ« π
θ
π³ = ππ«
180°

θ
360°

8. CIRCULAR RING
Where π« is the radius for inner circle,
π is the radius for outer circle.
π΄ππΈπ΄ = π(πΉ2 − π« π )

9. ELLIPSE
Where π«1 & π«2 is the radius for 1st and 2nd circle.
π΄ππΈπ΄ = ππ«1 π«2

10.

TRAPEZOID/TRAPEZIUM

Where π & π are parrallel sides
Where π & π are slant sides
Where π‘ is the perpendicular distance
1
π΄ππΈπ΄ = (π + π) × π
2
ππΈππΌππΈππΈπ = π + π + π + π

11.

RHOMBUS

Where π1 π2 are diagonals, π is the base
π‘ is the height, πΊπ ππ  π πππ.
1
π΄ππΈπ΄ = π1 π2 = π × π
2
ππΈππΌππΈππΈπ = 4 × πΊπ = π (π1 π + π2 π )
π
πΊπ =
(π1 π + π2 π ) = πΊπππ ππ πΉππππππ
π

12.

SPHERE
ππ’πππππ π΄πππ = 4ππ« 2
4ππ« 3
ππππ’ππ =
3

13.

HEMISPHERE

πππ‘ππ ππ’πππππ π΄πππ = 3ππ« 2
πΆπ’ππ£ππ ππ’πππππ π΄πππ = 2ππ« 2
2

ππππ’ππ = ππ« 3
3

14.

RECTANGULAR BOX
Where π, π, π are the three sides of the Box.
π΄πππ = πππ + πππ + πππ
ππππ’ππ = πππ

15.

CONE
Where π« is the radius (of the top), π‘ is the height
Where π is the radius base of the frustum
Where π₯ is slant height of the frustum or cone .
Right Circular Cone
π΄πππ = ππ2 + πππ
πΆπ’ππ£ππ ππ’ππππ π΄πππ = πππ = ππ( π‘2 + π« 2 )
π΄πππ ππ π‘ππ πππ π = ππ2
π ππππ‘ ππππππ‘ ππ ππππ (π₯) = π‘2 + π« 2
1

ππππ’ππ = ππ2 π
3

Frustum of a Cone
π΄πππ = π[ πΉ2 + π2 + π πΉ + π ]
πΆπ’ππ£ππ ππ’ππππ π΄πππ = π(πΉ + π)π
π΄πππ ππ π‘ππ πππ π = π πΉ2 + π2
πππππ‘ ππππππ‘ (π₯) =
1

π‘2 + (π + π«)2

ππππ’ππ = ππ(π« 2 + ππΉ + π2 )
3

16.

CUBE
Where π is the side of the cube
π΄πππ = 6π2
ππππ’ππ = π3

17.

CUBOID
Where π is the side, π is the base, and π‘ is the height
π΄πππ = 2(ππ + ππ + ππ)
ππππ’ππ = π × π × π
π·πππππππ =

18.

π2 + π2 + π2

ELLIPSOID
Where π1 π2 π3 are the radii
4

ππππ’ππ = ππ1 π2 π3
3

19.

CYLINDER
Where π is radius and π‘ is the height
π΄πππ = 2ππ(π + π)
ππππ’ππ = πππ π

πΆπ’ππ£ππ ππ’πππππ π΄πππ = 2πππ
π΄πππ ππ π‘ππ 2 πππππ’πππ ππππ  = 2πππ

20.

PRISM
Where π is base, π‘ is the height and π slant height
Where π is the perimeter of the base
πΏππ‘ππππ π΄πππ = π × π
πππ‘ππ π΄πππ = 2π + πΏππ‘ππππ π΄πππ

Irregular prism
ππππ’ππ = πππ

Rectangular prism
ππππ’ππ = πππ

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