Mensuration 2D (Area & Perimeter)

Master this topic with zero to advance depth.

Sniper Mode: Surface Measurement

1. Triangles

  • Hero's Formula: Area = тИЪ(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2.
  • Equilateral: Area = (тИЪ3/4)a┬▓. Height = (тИЪ3/2)a.
  • Right Angle: 1/2 * Base * Height.

2. Quadrilaterals

  • Rectangle: Area = L x B. Peri = 2(L+B). Diag = тИЪ(L┬▓+B┬▓).
  • Square: Area = a┬▓ or d┬▓/2. Peri = 4a.
  • Parallelogram: Base x Height.
  • Rhombus: 1/2 x d1 x d2. (All sides equal, diagonals bisect at 90).
  • Trapezium: 1/2 x (Sum of parallel sides) x Height.

3. Circle

  • Area: ╧Аr┬▓. (Pi = 22/7).
  • Circumference: 2╧Аr.
  • Semi-Circle: Area = ╧Аr┬▓/2. Peri = ╧Аr + 2r (Don't forget diameter!).

4. Sniper Tricks

  • Path outside: Area = (L + B + 2w) * 2w.
  • Path inside: Area = (L + B - 2w) * 2w.
  • Path cross: Area = (L + B - w) * w.