Rectangle
A rectangle is a quadrilateral with four right angles. Opposite sides are equal and parallel.
Properties
A rectangle is a parallelogram with all angles equal to 90°. It is a special case of a parallelogram where all angles are right angles. A square is a special case of a rectangle where all sides are equal.
Basic Formulas
S = a · b
Area (width × height)
P = 2(a + b)
Perimeter (twice the sum of sides)
d = √(a² + b²)
Diagonal (Pythagorean theorem)
R = √(a² + b²) / 2
Circumradius (half the diagonal)
Example
Given: width a = 8 cm, height b = 5 cm
Area: S = 8 · 5 = 40 cm²
Perimeter: P = 2(8 + 5) = 2 · 13 = 26 cm
Diagonal: d = √(8² + 5²) = √(64 + 25) = √89 ≈ 9.434 cm
Circumradius: R = 9.434 ÷ 2 ≈ 4.717 cm
Golden Rectangle
A golden rectangle has side lengths in the golden ratio φ = (1 + √5) / 2 ≈ 1.618. It is considered aesthetically pleasing and appears frequently in art and architecture.