Mensuration 2D: Formula Sheet
Area & Perimeter Reference
1. Quadrilaterals
| Shape | Area (A) | Perimeter (P) |
|---|---|---|
| Rectangle (l = length, b = breadth) |
$$ l \times b $$ | $$ 2(l + b) $$ |
| Square (a = side) |
$$ a^2 $$ | $$ 4a $$ |
| Parallelogram (b = base, h = height) |
$$ b \times h $$ | $$ 2(a + b) $$ |
| Rhombus (d1, d2 = diagonals) |
$$ \frac{1}{2} d_1 d_2 $$ | $$ 4a $$ |
| Trapezium (a, b = parallel sides) |
$$ \frac{1}{2} (a + b)h $$ | Sum of all sides |
2. Triangles
| Type | Formula |
|---|---|
| General Triangle (Base & Height) |
$$ Area = \frac{1}{2} \times base \times height $$ |
| Heron’s Formula (Given 3 sides a, b, c) |
$$ Area = \sqrt{s(s-a)(s-b)(s-c)} $$ where $$ s = \frac{a+b+c}{2} $$ |
| Equilateral Triangle (Side ‘a’) |
$$ Area = \frac{\sqrt{3}}{4} a^2 $$ $$ Height = \frac{\sqrt{3}}{2} a $$ |
3. Circles
Full Circle
Area: $$ \pi r^2 $$
Circumference: $$ 2 \pi r $$
Semi-Circle
Area: $$ \frac{1}{2} \pi r^2 $$
Perimeter: $$ \pi r + 2r $$