Square Pyramid

Written by Jerry Ratzlaff on . Posted in Solid Geometry

  • square pyramid 2square pyramid1 base
  • 8 edges
  • 4 side faces
  • 5 vertexs

Base Area of a Square Pyramid formula

\(\large{ A_b= a^2 }\)

Where:

\(\large{ A_b }\) = base area

\(\large{ a }\) = edge

Edge of a Square Pyramid formula

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

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

Where:

\(\large{ a }\) = edge

\(\large{ h }\) = height

\(\large{ A_f }\) = face area

\(\large{ A_l }\) = lateral surface area

Height of a Square Pyramid formula

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

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

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

\(\large{ h =   3\; \frac{V}{a_2}   }\)

Where:

\(\large{ h }\) = height

\(\large{ A_f }\) = face area

\(\large{ A_s }\) = surface area

\(\large{ A_l }\) = lateral surface area

\(\large{ a }\) = edge

\(\large{ V }\) = volume

Face Area of a Square Pyramid formula

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

Where:

\(\large{ A_f}\) = face area

\(\large{ a }\) = edge

\(\large{ h }\) = height

Lateral Surface Area of a Square Pyramid formula

\(\large{ A_l = a \sqrt {a^2\; 4\;h^2 }   }\)

Where:

\(\large{ A_l }\) = lateral surface area

\(\large{ a }\) = edge

\(\large{ h }\) = height

Surface Area of a Square Pyramid formula

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

Where:

\(\large{ A_s }\) = surface area

\(\large{ a }\) = edge

\(\large{ h }\) = edge

Volume of a Square Pyramid formula

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

Where:

\(\large{ V }\) = volume

\(\large{ a }\) = edge

\(\large{ h }\) = height