TMSCA Formulas

Circumference of a Circle

π\*d (d=diameter)

Area of a Circle

πr² (r=radius)

Area of a Square w/ Diagonal

d²/2 (d=diagonal)

Area of a Parallelogram

b\*h (b=base & h=height)

Area of a Trapezoid

1/2h(b₁+b₂) (b₁ is the bottom edge and b₂ is the top edge)

Area of a Triangle

bh/2

Area of a Rhombus

d₁\*d₂/2 (d₁=up and down diagonal) (d₂=left and right diagonal)

Area of Scalene Triangle (Heron's Formula)

√s(s - a)(s - b)(s - c) (abc - sides of triangle, s- semiperimeter)

Semipermeter

a+b+c/2

Area of an Equilateral Triangle (w/ Side)

(s²\*√3)/4

Area of an Equilateral Triangle (w/ Height)

(h²√3)/3

Height of an Equilateral Triangle (given side)

(s√3)/2

Diagonal of a Square

side√2

Area of Any Regular Polygon (w/number and length of sides)

ns²/4 tan(180/n) (n=number of sides and s= length of sides)

Area of Any Regular Polygon (w/perimeter and apothem)

pa/2 (p=perimeter and a= apothem)

Inner Diagonal of cube

side√3

Surface Area of a Cube (w/ edge)

6e² (e=edge)

Surface Area of a Cube (w/ inner diagonal)

d²\*2 (d=inner diagonal)

Surface Area of a Cube (w/ volume)

6v²/3 (volume)

Surface Area of Rectangular Prism

2(lw+lh+wh)

Inner Diagonal of a Rectangular Solid

√L²+w²+h²

Lateral Surface Area of a Cylinder

2πrh (r\=radius and h\=height)

Lateral Surface Area of a Cone

√r²+h²

Total Surface Area of a Cylinder

2πr(r+h)

Total Surface Area of a Cone (given slant height

πr(r+s) (s\=slant height)

Surface Area of a Sphere

4πr²

Surface Area of a Hemisphere

3πr²

Volume of a Cube (given edge)

e³ (e\=edge)

Volume of a Rectangular Prism

l*w*h

Volume of a Cylinder

πr²h

Volume of a Cone (given radius & height)

πr²h/3 (h\= height, r\=radius)

Volume of a Cone (given diameter & height)

1/12*πd²h (h\=height, d\=diameter)

Volume of a Sphere

4πr^3/3

Volume of a Hemisphere

(2/3)πr^3

Volume of a Pyramid

bh/3 (b\=area of base and h\=height)

Total Number of Subsets or Power Set

2^n (number of elements)

Number of Proper Subsets

2^n-1 (number of elements)

Permutations (Ways something can be arranged in an order)

n! ÷ (n-r)! (n\=total number of objects and r\=number of objects selected)

Total of Sequences

n(n+2)/4 (n=last number)

Combinations (Ways something can be arranged w/o order in mind)

n!/r!(n-r)! (n\=total number of objects and r\=number of objects selected)

Work of Two People Combined

n*n/n+n

Sum of roots in Quadratic

-b/a

Product of Roots in Quadratics

c/a

Axis of Symmetry

-b/2a

Volume of a cube (given Inner diagonal)

(3√d)*3 (d\=inner diagonal)

Midpoint of two points

(x1 + x2)/2, (y1 + y2)/2

Midrange

Highest number+Lowest number/2

Interior Angle of a Regular Polygon

(n-2)180 (number of sides)

Number of Diagonals in a Polygon

((n-3)n)/2 (n=number of vertices or sides)

Geometric Mean

√ab (a=one number, b=second number)

Exterior angle of a regular polygon

360/number of sides

Number of diagonals from one vertex

n-3 (n=number of sides or vertices)

Simple Interest

prt

Triangular Number

n(n+1)/2