Right Square Pyramid

Written by Jerry Ratzlaff on . Posted in Solid Geometry

  • square pyramid 2right square pyramid 2Right square pyramid (a three-dimensional figure) has a square base and the apex alligned above the center of the base.
  • 1 base
  • 8 edges
  • 4 faces
  • 5 vertexs

Base Area of a Right Square Pyramid formula

\(\large{ A_b =  a^2   }\)

Where:

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

\(\large{ a }\) = edge

Edge of a Right Square Pyramid formula

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

Where:

\(\large{ a }\) = edge

\(\large{ h }\) = height

\(\large{ V }\) = volume

Height of a Right Square Pyramid formula

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

Where:

\(\large{ h }\) = height

\(\large{ a }\) = edge

\(\large{ V }\) = volume

Face Area of a Right Square Pyramid formula

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

Where:

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

\(\large{ a }\) = edge

\(\large{ h }\) = height

Lateral Surface Area of a Right Square Pyramid formula

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

Where:

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

\(\large{ a }\) = edge

\(\large{ h }\) = height

Surface Area of a Right Square Pyramid formula

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

Where:

\(\large{ A_s }\) = surface area (bottom, sides)

\(\large{ a }\) = edge

\(\large{ h }\) = edge

Volume of a Right Square Pyramid formula

\(\large{ V=  a^2\;  \frac{h}{3} }\)

Where:

\(\large{ V }\) = volume

\(\large{ a }\) = edge

\(\large{ h }\) = height