2D Geometric Shapes Reference
Complete formulas and properties for common plane geometry shapes.
Circle
Properties:
- Area: A = πr²
- Circumference: C = 2πr = πd
- Diameter: d = 2r
Where r = radius, d = diameter
Square
Properties:
- Area: A = s²
- Perimeter: P = 4s
- Diagonal: d = s√2
Where s = side length
Rectangle
Properties:
- Area: A = l × w
- Perimeter: P = 2(l + w)
- Diagonal: d = √(l² + w²)
Where l = length, w = width
Triangle (General)
Heron's Formula:
- Area: A = √(s(s-a)(s-b)(s-c))
- Semiperimeter: s = (a+b+c)/2
- Perimeter: P = a + b + c
Where a, b, c are side lengths
Right Triangle
Pythagorean Theorem:
- c² = a² + b²
- Area: A = (a × b)/2
- Perimeter: P = a + b + c
Where c = hypotenuse, a, b = legs
Equilateral Triangle
Properties:
- Area: A = (√3/4)s²
- Perimeter: P = 3s
- Height: h = (√3/2)s
Where s = side length
Isosceles Triangle
Properties:
- Area: A = (b × h)/2
- Height: h = √(s² - (b/2)²)
- Perimeter: P = 2s + b
Where s = equal sides, b = base
Parallelogram
Properties:
- Area: A = base × height
- Perimeter: P = 2(a + b)
Where a, b = adjacent sides
Rhombus
Properties:
- Area: A = (d₁ × d₂)/2
- Side: s = √((d₁/2)² + (d₂/2)²)
- Perimeter: P = 4s
Where d₁, d₂ = diagonals
Regular Polygon
Properties:
- Area: A = (P × a)/2
- Perimeter: P = n × s
- Apothem: a = s/(2×tan(π/n))
Where n = sides, s = side length
Annulus (Ring)
Properties:
- Area: A = π(R² - r²)
- Outer circumference: C₁ = 2πR
- Inner circumference: C₂ = 2πr
Where R = outer radius, r = inner radius
Stadium
Properties:
- Area: A = 2ra + πr²
- Perimeter: P = 2a + 2πr
Where a = length, r = radius of ends
Important Formulas & Theorems
Distance Formula
d = √((x₂-x₁)² + (y₂-y₁)²)
Law of Cosines
c² = a² + b² - 2ab·cos(C)
Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
Constants
π ≈ 3.14159265359
√2 ≈ 1.41421356237
√3 ≈ 1.73205080757