Formulas for 2D and 3D Shapes

Square Area

A = s² (where s is the side length)

Square Perimeter

P = 4s

Rectangle Area

A = lw (where l is length and w is width)

Rectangle Perimeter

P = 2l + 2w

Triangle Area

A = (1/2)bh (where b is base and h is height)

Triangle Perimeter

P = a + b + c (where a, b, and c are side lengths)

Circle Area

A = πr² (where r is radius)

Circle Circumference

C = 2πr = πd (where d is diameter)

Trapezoid Area

A = (1/2)h(b₁ + b₂) (where h is height, b₁ and b₂ are base lengths)

Parallelogram Area

A = bh (where b is base and h is height)

Parallelogram Perimeter

P = 2a + 2b (where a and b are side lengths)

Cube Surface Area

SA = 6s² (where s is side length)

Cube Volume

V = s³

Cuboid Surface Area

SA = 2ab + 2ac + 2bc (where a, b, and c are side lengths)

Cuboid Volume

V = abc

Sphere Surface Area

SA = 4πr² (where r is radius)

Sphere Volume

V = (4/3)πr³

Cylinder Surface Area

SA = 2πr² + 2πrh (where r is radius, h is height)

Cylinder Volume

V = πr²h

Cone Surface Area

SA = πr² + πrl (where r is radius, l is slant height)

Cone Volume

V = (1/3)πr²h (where h is height)

Pyramid Surface Area

SA = base area + (1/2) * perimeter of base * slant height

Pyramid Volume

V = (1/3) * base area * height

Pythagorean Theorem

a² + b² = c² (for right triangles, where c is the hypotenuse)

Distance Formula

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Slope Formula

m = (y₂ - y₁) / (x₂ - x₁) (for finding the slope of a line)