Right Rectangular Prism

• Right rectangular prism (a three-dimensional figure) has six faces that are rectangles with equal sides and equal angles also called a right square prism.
• Diagonal is a line from one vertices to another that is non adjacent.
• 2 bases
• 12 edges
• 4 side faces
• 8 vertexs
• 4 base diagonals
• 8 face diagonals
• 4 space diagonals

Diagonal of a Right Rectangular Prism formula

\(\large{ D' = \sqrt {a^2 + b^2 + h^2} }\)

Where:

\(\large{ D' }\) = space diagonal

\(\large{ a, b }\) = edge

\(\large{ h }\) = height

Edge of a Right Rectangular Prism formula

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

\(\large{ a = \sqrt {D'^2 - h^2 - b^2} }\)

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

\(\large{ b = \sqrt {D'^2 - h^2 - a^2} }\)

Where:

\(\large{ a, b }\) = edge

\(\large{ h }\) = height

\(\large{ D' }\) = space diagonal

\(\large{ V }\) = volume

Height of a Right Rectangular Prism formula

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

\(\large{ h = \sqrt {D'^2 - b^2 - a^2} }\)

Where:

\(\large{ h }\) = height

\(\large{ a, b }\) = edge

\(\large{ D' }\) = space diagonal

\(\large{ V }\) = volume

Surface Area of a Right Rectangular Prism formula

\(\large{ A_s = 2\; \left( a\;b + a\;h +b\;h \right) }\)

Where:

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

\(\large{ a, b }\) = edge

\(\large{ h }\) = height

Volume of a Right Rectangular Prism formula

\(\large{ V= a\;b\;h }\)

Where:

\(\large{ V }\) = volume

\(\large{ a, b }\) = edge

\(\large{ h }\) = height