Mensuration – 2D

Rectangle

Area = l × b, Perimeter = 2(l + b), Diagonal = √(l² + b²)

Square

Area = a² = d²/2, Perimeter = 4a

Triangle

Area = ½ × base × height

Heron's formula

Area = √[s(s − a)(s − b)(s − c)], s = (a + b + c)/2

Equilateral triangle

Area = (√3/4)a², height = (√3/2)a

Circle

Area = πr², Circumference = 2πr

π ≈ 22/7 ≈ 3.14

Sector

Area = (θ/360) × πr², Arc = (θ/360) × 2πr

Parallelogram

Area = base × height

Rhombus

Area = ½ × d₁ × d₂

Trapezium

Area = ½ × (a + b) × h

Interior angle of regular polygon

(n − 2) × 180° / n

Sum of exterior angles = 360°

Diagonals of a polygon

n(n − 3)/2