All.mathematical tables, mensuration tables and formulae

Answer 1

Sure! Below is a collection of common mathematical tables, formulas, and concepts related to mensuration and basic geometry. This is not exhaustive but covers a range of essential topics:

1. Basic Geometry Formulas

Area Formulas

• Square:
  \[ A = a^2 \]
  (where \(a\) is the length of the side)

• Rectangle:
  \[ A = l \times b \]
  (where \(l\) is length and \(b\) is breadth)

• Triangle:
  \[ A = \frac{1}{2} \times b \times h \]
  (where \(b\) is the base and \(h\) is the height)

• Parallelogram:
  \[ A = b \times h \]
  (where \(b\) is the base and \(h\) is the height)

• Trapezium:
  \[ A = \frac{1}{2} \times (a + b) \times h \]
  (where \(a\) and \(b\) are the lengths of the parallel sides, and \(h\) is the height)

• Circle:
  \[ A = \pi r^2 \]
  (where \(r\) is the radius)

Perimeter Formulas

• Square:
  \[ P = 4a \]

• Rectangle:
  \[ P = 2(l + b) \]

• Triangle:
  \[ P = a + b + c \]
  (where \(a\), \(b\), and \(c\) are the lengths of the sides)

• Circle (Circumference):
  \[ C = 2\pi r \]

2. 3D Shapes Formulas

Volume Formulas

• Cube:
  \[ V = a^3 \]

• Rectangular Prism (Cuboid):
  \[ V = l \times b \times h \]

• Cylinder:
  \[ V = \pi r^2 h \]
  (where \(r\) is the radius, \(h\) is the height)

• Sphere:
  \[ V = \frac{4}{3} \pi r^3 \]

• Cone:
  \[ V = \frac{1}{3} \pi r^2 h \]

Surface Area Formulas

• Cube:
  \[ SA = 6a^2 \]

• Rectangular Prism:
  \[ SA = 2(lb + bh + hl) \]

• Cylinder:
  \[ SA = 2\pi r(h + r) \]

• Sphere:
  \[ SA = 4\pi r^2 \]

• Cone:
  \[ SA = \pi r(l + r) \]
  (where \(l\) is the slant height)

3. Trigonometric Ratios

Basic Ratios

• Sine:
  \[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \]

• Cosine:
  \[ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \]

• Tangent:
  \[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]

Trigonometric Identities

• \[ \sin^2(\theta) + \cos^2(\theta) = 1 \]

• \[ 1 + \tan^2(\theta) = \sec^2(\theta) \]

• \[ 1 + \cot^2(\theta) = \csc^2(\theta) \]

4. Important Constants

• π (Pi): Approximately 3.14 or \( \frac{22}{7} \)
• Euler's Number (e): Approximately 2.718

5. Units of Measurement

• Area:

  • Square units (m², cm², etc.)

• Volume:

  • Cubic units (m³, cm³, etc.)

• Length:

  • meters (m), centimeters (cm), kilometers (km), etc.

This summary covers basic formulas used in mensuration and geometry. If you have any specific topics or areas of interest, feel free to ask!