Useful Formulas

Plane Geometry (2D)

Right Triangle: (Pythagorean Theorem):

If c is the hypotenuse and a and b are the other sides then

Similar Triangles: Corresponding sides are in proportion.

2D Geometry	Area	Circumference (perimeter)
Triangle:	A = 1/2bh	P = a + b+ c
Equilateral triangle:	h = s , A = s2	P = 3s
Rectangle:	A = lw	P = 2l +2w
Parallelogram	A = bh	P = 2l +2w
Trapezoid:	A = 1/2h(a + b)
Circle:	A = πr2	C = 2πr

 

Solid Geometry 3D	Volume	Surface Area
Rectangular box:	V = lwh	S = 2 ( hl +lw + hw)
Sphere:	V = π r3	S = 4 πr2
Right Circular Cylinder:	V = πr2h	S = 2πrh + 2 πr2
Right Circular Cone	V = 1/3 πr2h	S = πr

Analytic Geometry: Distance between points (x₁ , y₁) and (x₂ , y₂) s=

From Trigonometry: Double Angle Formulas: sin 2u = 2 sin u cos u

and cos 2u = cos² u - sin² u = 1 - 2 sin² u = 2 cos ² u - 1