RMS Important Maths Formulas

Important Maths Formulas

Circle

• Area

  • Formula: $A = \pi r^2$

• Circumference

  • Formula: $C = 2\pi r$

• Diameter

  • Formula: $d = 2r$

Square

• Area

  • Formula: $A = a^2$

• Perimeter

  • Formula: $P = 4a$

• Diagonal

  • Formula: $d = a\sqrt{2}$

Rectangle

• Area

  • Formula: $A = l \times b$

• Perimeter

  • Formula: $P = 2(l + b)$

• Diagonal

  • Formula: $d = \sqrt{l^2 + b^2}$

Triangles

• General Triangle

  • Area

  • Formula: $A = \frac{1}{2} b h$

• Equilateral Triangle

  • Area

  • Formula: $A = \frac{\sqrt{3}}{4} a^2$

• Isosceles Triangle

  • Height Calculation

  • Formula: $h = \sqrt{a^2 - \frac{b^2}{4}}$

  • Area

  • Formula: $A = \frac{1}{2} b h$

• Right Triangle

  • Area

  • Formula: $A = \frac{1}{2} ab$

• Height of Any Triangle

  • Formula: $h = \frac{2A}{b}$

Trapezium

• Area

  • Formula: $A = \frac{1}{2}(a + b)h$

• Height Calculation

  • Formula: $h = \frac{2A}{a + b}$

Cube

• Volume

  • Formula: $V = a^3$

• Total Surface Area (TSA)

  • Formula: $TSA = 6a^2$

• Lateral Surface Area (LSA)

  • Formula: $LSA = 4a^2$

• Diagonal

  • Formula: $d = a\sqrt{3}$

Cuboid

• Volume

  • Formula: $V = lbh$

• Total Surface Area (TSA)

  • Formula: $TSA = 2(lb + bh + hl)$

• Lateral Surface Area (LSA)

  • Formula: $LSA = 2h(l + b)$

• Diagonal

  • Formula: $d = \sqrt{l^2 + b^2 + h^2}$

Cylinder

• Volume

  • Formula: $V = \pi r^2 h$

• Curved Surface Area (CSA)

  • Formula: $CSA = 2\pi r h$

• Total Surface Area (TSA)

  • Formula: $TSA = 2\pi r(h + r)$

Right-Angled Triangle (Pythagoras)

• Sides:

  • Hypotenuse is the longest side (opposite right angle)

  • Other sides are Base and Height/Perpendicular

• Main Formula (Pythagorean Theorem)

  • Formula: $\text{Hypotenuse}^2 = \text{Base}^2 + \text{Height}^2$

Finding Lengths in Right-Angled Triangle

• To find Hypotenuse: If Base = b, Height = h, then

  • Formula: $\text{Hypotenuse} = \sqrt{b^2 + h^2}$

• To find Base: If Hypotenuse = c, Height = h, then

  • Formula: $b = \sqrt{c^2 - h^2}$

• To find Height (Perpendicular): If Hypotenuse = $c$ , Base = $b$ , then

  • Formula: $h = \sqrt{c^2 - b^2}$

Polygons

• Interior Angles

  • Sum of Interior Angles: For a polygon with $n$ sides

  • Formula: $S = (n - 2) \times 180^{\circ}$

  • Each Interior Angle (for regular polygons): For a regular polygon with $n$ sides

  • Formula: $A = \frac{(n - 2) \times 180^{\circ}}{n}$

• Exterior Angles

  • Sum of Exterior Angles: For any convex polygon

  • Formula: $S = 360^{\circ}$

  • Each Exterior Angle (for regular polygons): For a regular polygon with $n$ sides

  • Formula: $A=\frac{360}{n}$