Area measures the surface enclosed by a plane figure; perimeter is the length of its boundary.
1Rectangles and squares
Rectangle: area = l × b, perimeter = 2(l + b), diagonal = √(l² + b²)
Square: area = a² = d²/2, perimeter = 4a, diagonal = a√2
2Triangles
Area = ½ × base × height
Heron's formula: area = √[s(s − a)(s − b)(s − c)], s = (a + b + c)/2
Equilateral: area = (√3/4)a²
3Circles
Area = πr², circumference = 2πr
Sector of angle θ: area = (θ/360) × πr², arc = (θ/360) × 2πr
4Paths and changes
Path of width w outside an l × b rectangle: area = 2w(l + b + 2w)
Sides increased by x%: area increases by (2x + x²/100)%