Square Pyramid

Written by Jerry Ratzlaff on . Posted in Solid Geometry

 

square pyramid 2

square pyramid

  • 1 base
  • 8 edges
  • 4 side faces
  • 5 vertexs

Edge formula

\(a = \sqrt   {   \sqrt {4h^4 + A_{l } {^2} }   - 2h^2     } \)

\(a = \sqrt   { 2     \sqrt {h^4 + 4A_{f } {^2} }   - 2h^2     } \)

Where:

\(a\) = edge

\(h\) = height

\(A_f\) = face area

\(A_l\) = lateral surface area

Height formula

\(h = \frac{1}{2} \sqrt { 16 \left( \frac {A_f } {a} \right)^2 -a^2 } \)

\(h = \frac{1}{2} \sqrt { \left( \frac {A_l } {a} \right)^2 -a^2 } \)

\(h = \frac{1}{2} \sqrt { A_s { \left( -2 \frac {A_s } {a^2} \right) } } \)

\(h =   3 \frac{V}{a_2}   \)

Where:

\(h\) = height

\(A_f\) = face area

\(A_s\) = surface area

\(A_l\) = lateral surface area

\(a\) = edge

\(V\) = volume

Face Area formula

\(A_f = \frac{a}{2} \sqrt   {\frac {a^2 } {4}   +h^2 } \)

Where:

\(A_f\) = face area

\(a\) = edge

\(h\) = height

Lateral Surface Area formula

\(A_l = a \sqrt {a^2 4h^2 }   \)

Where:

\(A_l\) = lateral surface area

\(a\) = edge

\(h\) = height

Base Area formula

\(A_b= a^2 \)

Where:

\(A_b\) = base area

\(a\) = edge

Lateral Surface Area formula

\(A_l= a \sqrt {a^2 + 4h^2 }   \)

Where:

\(A_l\) = surface area

\(a\) = edge

\(h\) = edge

Surface Area formula

\(A_s= a^2+2a \sqrt {\frac {a^2} {4} +h^2 }   \)

Where:

\(A_s\) = surface area

\(a\) = edge

\(h\) = edge

Volume formula

\(V= a^2 \; \frac{h}{3}\)

Where:

\(V\) = volume

\(a\) = edge

\(h\) = height