Geometry Formulas Reference

Complete collection of essential geometry formulas for area, perimeter, volume, and surface area calculations. Your ultimate reference guide.

Quick Reference Symbols

A = Area

P = Perimeter

V = Volume

SA = Surface Area

r = radius

d = diameter

h = height

b = base

l = length

w = width

s = side

π = 3.14159...

2D Shapes (Plane Figures)

Rectangle

Area:

A = l × w

Perimeter:

P = 2(l + w)

Example:

Rectangle with length = 8 cm, width = 5 cm

Area = 8 × 5 = 40 cm²

Perimeter = 2(8 + 5) = 26 cm

Circle

Area:

A = π × r²

Circumference:

C = 2π × r

Diameter:

d = 2r

Example:

Circle with radius = 6 cm

Area = π × 6² = 36π ≈ 113.1 cm²

Circumference = 2π × 6 = 12π ≈ 37.7 cm

Diameter = 2 × 6 = 12 cm

Triangle

Area:

A = ½ × b × h

Perimeter:

P = a + b + c

Heron's Formula:

A = √[s(s-a)(s-b)(s-c)]

where s = (a+b+c)/2

Example:

Triangle with base = 10 cm, height = 6 cm

Area = ½ × 10 × 6 = 30 cm²

Triangle with sides 3, 4, 5 cm:

Perimeter = 3 + 4 + 5 = 12 cm

Square

Area:

A = s²

Perimeter:

P = 4s

Diagonal:

d = s√2

Example:

Square with side = 7 cm

Area = 7² = 49 cm²

Perimeter = 4 × 7 = 28 cm

Diagonal = 7√2 ≈ 9.9 cm

Parallelogram

Area:

A = b × h

Perimeter:

P = 2(a + b)

Example:

Parallelogram with base = 12 cm, height = 4 cm

Area = 12 × 4 = 48 cm²

Note: Height is perpendicular distance between parallel sides

Trapezoid

Area:

A = ½(b₁ + b₂) × h

Perimeter:

P = a + b₁ + c + b₂

Example:

Trapezoid with parallel sides 8 cm, 12 cm and height 5 cm

Area = ½(8 + 12) × 5 = 50 cm²

b₁ and b₂ are the parallel sides

3D Shapes (Solid Figures)

Cube

Volume:

V = s³

Surface Area:

SA = 6s²

Example:

Cube with side = 4 cm

Volume = 4³ = 64 cm³

Surface Area = 6 × 4² = 96 cm²

Rectangular Prism

Volume:

V = l × w × h

Surface Area:

SA = 2(lw + lh + wh)

Example:

Prism with l = 6 cm, w = 4 cm, h = 3 cm

Volume = 6 × 4 × 3 = 72 cm³

SA = 2(24 + 18 + 12) = 108 cm²

Cylinder

Volume:

V = π × r² × h

Surface Area:

SA = 2π × r × (r + h)

Example:

Cylinder with radius = 3 cm, height = 8 cm

Volume = π × 3² × 8 = 72π ≈ 226.2 cm³

SA = 2π × 3 × (3 + 8) = 66π ≈ 207.3 cm²

Sphere

Volume:

V = ⁴⁄₃ × π × r³

Surface Area:

SA = 4π × r²

Example:

Sphere with radius = 5 cm

Volume = ⁴⁄₃ × π × 5³ ≈ 523.6 cm³

Surface Area = 4π × 5² ≈ 314.2 cm²

Cone

Volume:

V = ⁱ⁄₃ × π × r² × h

Surface Area:

SA = π × r × (r + l)

where l = slant height

Example:

Cone with radius = 4 cm, height = 9 cm

Volume = ⁱ⁄₃ × π × 4² × 9 ≈ 150.8 cm³

Slant height l = √(r² + h²) = √(16 + 81) ≈ 9.85 cm

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