Area & Perimeter

Square

Area A = a²

Perimeter P = 4a

Rectangle

Area A = l × w

Perimeter P = 2(l + w)

Parallelogram

Area A = b × h

Perimeter P = 2(b + s)

Rhombus

Area A = p × q ÷ 2

Perimeter P = 4 × √((p/2)² + (q/2)²)

Trapezoid (trapezium)

Area A = (a + b) ÷ 2 × h

Perimeter P = a + b + c + d

Kite

Area A = p × q ÷ 2

Perimeter P = 2(a + b)

Triangle — three sides

Area A = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2

Perimeter P = a + b + c

Triangle — base and height

Area A = b × h ÷ 2

Perimeter P = b + two slanted sides

Right triangle

Area A = a × b ÷ 2

Perimeter P = a + b + √(a² + b²)

Isosceles triangle

Area A = b × h ÷ 2, h = √(s² − (b/2)²)

Perimeter P = b + 2s

Equilateral triangle

Area A = (√3 ÷ 4) × a²

Perimeter P = 3a

Triangle — two sides and the angle between

Area A = ½ × a × b × sin C

Perimeter P = a + b + c, c = √(a² + b² − 2ab cos C)

Circle

Area A = π r²

Perimeter C = 2 π r

Semicircle

Area A = π r² ÷ 2

Perimeter P = π r + 2r

Quarter circle

Area A = π r² ÷ 4

Perimeter P = π r ÷ 2 + 2r

Sector (pie slice)

Area A = (θ ÷ 360) × π r²

Perimeter P = (θ ÷ 360) × 2 π r + 2r

Circular segment (arch)

Area A = ½ r² (θ − sin θ), θ in radians

Perimeter P = r θ + 2 r sin(θ/2)

Ring (annulus)

Area A = π (R² − r²)

Perimeter P = 2π (R + r) (both edges)

Ellipse (oval)

Area A = π a b

Perimeter P ≈ π [3(a + b) − √((3a + b)(a + 3b))]

Regular polygon (pentagon, hexagon, octagon…)

Area A = n s² ÷ (4 tan(180° ÷ n))

Perimeter P = n s

L-shape

Area A = L × W − l × w

Perimeter P = 2(L + W)

Any polygon — by corner points

Area A = ½ |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)|

Perimeter P = Σ √((xᵢ₊₁ − xᵢ)² + (yᵢ₊₁ − yᵢ)²)