Preston Meadow's Height Enhancement Blog

equilateral triangle height formula

What are the formulas for calculating diameter of a circle, height and side length of equilateral triangle?

Also surface area and edge length of cube and radius of a sphere?

Circle
A = πr²
length of chord
L = 2√(r²-d²)
r = radius
d = perpendicular distance from chord to center
Area of a segment
A = (r²/2)[(π/180)θ – sinθ]
equation of circle with center at a,b and radius r
(x–a)² + (y–b)² = r²
center at the origin
x² + y² = r²

cylinder V = πr²h
A = 2πr² + 2πrh = 2πr(r+h)

equalaterial triangle
A = s²√3/4
any triangle
A = √[s(s–a)(s–b)(s–c)]
where s = (a+b+c)/2
a,b,c are the sides of the triangle

sphere
V = ⁴/₃πr³
A = 4πr²
Volume of a partial sphere
V = (π/3)y²(3r – y)
y is height of filled portion.

Volume square base pyramid, or any base
V = 1/3 Bh
B is area of base
h is perpendicular height from base to apex
Surface area square base pyramid
A = Aʙ + ps/2
Aʙ is area of base
p is the perimeter of base
s is slant height

cone
surface area A = πr² + πrs = πr(r+s)
where s is slant height
volume V = ⅓πr²h, h is height of cone (not slant)
h² + r² = s²

octagon, with sides all equal,
A = 2(√2–1)a² ≈ 4.828a²
where a is the length of a side

square A = s²
rectangle A = L•W
cube V = s³
A = 6s²
cuboid (rectangular prism)
V = L•W•H
A = 2LW + 2LH + 2WH

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