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# Mathematical Formulars For College Students 647 views

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 𝐋 is the Side and 𝐃 the Diagonal
Where 𝐩 perpendicular distance to it from opp. vertices
 Normal
𝐴𝑅𝐸𝐴 = 2(𝐥 + 𝐛) × 𝐡
1 2
𝐴𝑅𝐸𝐴 = 𝑳 = 𝑫
2
2

𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 𝟒𝑳2 = 2𝑫2

1
𝐴𝑅𝐸𝐴 = 𝐃(𝐩𝟏 + 𝐩𝟐 )
2

2. RECTANGLE
Where 𝐥 is the lenght, 𝐛 the breadth, and 𝐡 is height

 Normal Rectangle
𝐴𝑅𝐸𝐴 = 𝐥 × 𝐛
𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 2(𝐥 + 𝐛)
 4 Walls of a Room
𝐴𝑅𝐸𝐴 = 2(𝐥 + 𝐛) × 𝐡

3. TRIANGLE
 Normal Triangle
Where 𝐛 is the base and 𝐡 the height ,
𝐚, 𝐛, 𝐜 are the sides of the triangle,
𝐬 is the semi − perimeter of the triangle.
1
𝐴𝑅𝐸𝐴 = 𝐛𝐡 =
2

𝐬 𝐬 − 𝐚 𝐬 − 𝐛 (𝐬 − 𝐜)

𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 𝒂 + 𝒃 + 𝒄 = 2𝒔
 Isoceles Triangle
𝒃
𝐴𝑅𝐸𝐴 =
𝟒𝐚𝟐 − 𝐛 𝟐
4
𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 2𝒂 + 𝒃
1
𝐻𝑒𝑖𝑔𝑕𝑡 (𝒉) =
𝟒𝐚𝟐 − 𝐛 𝟐
2

4. POLYGON
 Regular
𝐴𝑟𝑒𝑎 𝑜𝑓 𝐻𝑒𝑥𝑎𝑔𝑜𝑛 =

3 3 ÷ 2 × (𝑠𝑖𝑑𝑒𝑠)2

𝐴𝑟𝑒𝑎 𝑜𝑓 𝑂𝑐𝑡𝑎𝑔𝑜𝑛 = [2

2 + 1] × (𝑠𝑖𝑑𝑒𝑠)2

5. PARALLELOGRAM
Where 𝐛 is the base and 𝐚 slant ′diagonal′;
𝐡 is the corresponding attitude.

𝐴𝑅𝐸𝐴 = 𝐛𝐡
𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 𝟐𝐚 + 𝟐𝐛

6. CIRCLE
Where 𝐫 is the radius, 𝐝 is diameter,
𝐜 is the circumference of the circle.

2
2
𝐝
𝒄
1
2
𝐴𝑅𝐸𝐴 = 𝜋𝐫 = 𝜋
=
= (𝒄 × 𝐫)
4
4𝜋
2

𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 2𝜋𝐫 = Circumference of Circle

7. CIRCULAR SECTOR
Where 𝐫 is the radius, 𝐋 is the length of the sector.
𝐴𝑅𝐸𝐴 = 𝜋𝐫 𝟐
θ
𝑳 = 𝜋𝐫
180°

θ
360°

8. CIRCULAR RING
Where 𝐫 is the radius for inner circle,
𝐑 is the radius for outer circle.
𝐴𝑅𝐸𝐴 = 𝜋(𝑹2 − 𝐫 𝟐 )

9. ELLIPSE
Where 𝐫1 & 𝐫2 is the radius for 1st and 2nd circle.
𝐴𝑅𝐸𝐴 = 𝜋𝐫1 𝐫2

10.

TRAPEZOID/TRAPEZIUM

Where 𝐚 & 𝑏 are parrallel sides
Where 𝐜 & 𝑑 are slant sides
Where 𝐡 is the perpendicular distance
1
𝐴𝑅𝐸𝐴 = (𝒂 + 𝒃) × 𝒉
2
𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 𝒂 + 𝒃 + 𝒄 + 𝒅

11.

RHOMBUS

Where 𝒅1 𝒅2 are diagonals, 𝐛 is the base
𝐡 is the height, 𝑺𝒅 𝑖𝑠 𝑠𝑖𝑑𝑒.
1
𝐴𝑅𝐸𝐴 = 𝒅1 𝒅2 = 𝒃 × 𝒉
2
𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 4 × 𝑺𝒅 = 𝟐 (𝒅1 𝟐 + 𝒅2 𝟐 )
𝟏
𝑺𝒅 =
(𝒅1 𝟐 + 𝒅2 𝟐 ) = 𝑺𝒊𝒅𝒆 𝒐𝒇 𝑹𝒉𝒐𝒎𝒃𝒖𝒔
𝟐

12.

SPHERE
𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 4𝜋𝐫 2
4𝜋𝐫 3
𝑉𝑜𝑙𝑢𝑚𝑒 =
3

13.

HEMISPHERE

𝑇𝑜𝑡𝑎𝑙 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 3𝜋𝐫 2
𝐶𝑢𝑟𝑣𝑒𝑑 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 2𝜋𝐫 2
2

𝑉𝑜𝑙𝑢𝑚𝑒 = 𝜋𝐫 3
3

14.

RECTANGULAR BOX
Where 𝐚, 𝐛, 𝐜 are the three sides of the Box.
𝐴𝑟𝑒𝑎 = 𝟐𝒂𝒃 + 𝟐𝒂𝒄 + 𝟐𝒃𝒄
𝑉𝑜𝑙𝑢𝑚𝑒 = 𝒂𝒃𝒄

15.

CONE
Where 𝐫 is the radius (of the top), 𝐡 is the height
Where 𝐑 is the radius base of the frustum
Where 𝐥 is slant height of the frustum or cone .
Right Circular Cone
𝐴𝑟𝑒𝑎 = 𝜋𝒓2 + 𝜋𝒓𝒍
𝐶𝑢𝑟𝑣𝑒𝑑 𝑆𝑢𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 𝜋𝒓𝒍 = 𝜋𝒓( 𝐡2 + 𝐫 2 )
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡𝑕𝑒 𝑏𝑎𝑠𝑒 = 𝜋𝒓2
𝑠𝑙𝑎𝑛𝑡 𝑕𝑒𝑖𝑔𝑕𝑡 𝑜𝑓 𝑐𝑜𝑛𝑒 (𝐥) = 𝐡2 + 𝐫 2
1

𝑉𝑜𝑙𝑢𝑚𝑒 = 𝜋𝒓2 𝒉
3

Frustum of a Cone
𝐴𝑟𝑒𝑎 = 𝜋[ 𝑹2 + 𝒓2 + 𝒍 𝑹 + 𝒓 ]
𝐶𝑢𝑟𝑣𝑒𝑑 𝑆𝑢𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 𝜋(𝑹 + 𝒓)𝒍
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡𝑕𝑒 𝑏𝑎𝑠𝑒 = 𝜋 𝑹2 + 𝒓2
𝑆𝑙𝑎𝑛𝑡 𝑕𝑒𝑖𝑔𝑕𝑡 (𝐥) =
1

𝐡2 + (𝐑 + 𝐫)2

𝑉𝑜𝑙𝑢𝑚𝑒 = 𝜋𝒉(𝐫 2 + 𝒓𝑹 + 𝐑2 )
3

16.

CUBE
Where 𝒍 is the side of the cube
𝐴𝑟𝑒𝑎 = 6𝒍2
𝑉𝑜𝑙𝑢𝑚𝑒 = 𝒍3

17.

CUBOID
Where 𝒍 is the side, 𝐛 is the base, and 𝐡 is the height
𝐴𝑟𝑒𝑎 = 2(𝒍𝒃 + 𝒃𝒉 + 𝒉𝒍)
𝑉𝑜𝑙𝑢𝑚𝑒 = 𝒍 × 𝒃 × 𝒉
𝐷𝑖𝑎𝑔𝑜𝑛𝑎𝑙 =

18.

𝒍2 + 𝒃2 + 𝒉2

ELLIPSOID
Where 𝒓1 𝒓2 𝒓3 are the radii
4

𝑉𝑜𝑙𝑢𝑚𝑒 = 𝜋𝒓1 𝒓2 𝒓3
3

19.

CYLINDER
Where 𝒓 is radius and 𝐡 is the height
𝐴𝑟𝑒𝑎 = 2𝜋𝒓(𝒓 + 𝒉)
𝑉𝑜𝑙𝑢𝑚𝑒 = 𝜋𝒓𝟐 𝒉

𝐶𝑢𝑟𝑣𝑒𝑑 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 2𝜋𝒓𝒉
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡𝑕𝑒 2 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑒𝑛𝑑𝑠 = 2𝜋𝒓𝟐

20.

PRISM
Where 𝒃 is base, 𝐡 is the height and 𝒍 slant height
Where 𝒑 is the perimeter of the base
𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝐴𝑟𝑒𝑎 = 𝒑 × 𝒉
𝑇𝑜𝑡𝑎𝑙 𝐴𝑟𝑒𝑎 = 2𝒃 + 𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝐴𝑟𝑒𝑎

Irregular prism
𝑉𝑜𝑙𝑢𝑚𝑒 = 𝒃𝒉𝒍

Rectangular prism
𝑉𝑜𝑙𝑢𝑚𝑒 = 𝒂𝒃𝒄

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