# Right Rectangular Prism

on . Posted in Solid Geometry

• 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

$$\large{ D' = \sqrt {a^2 + b^2 + h^2} }$$
Symbol English Metric
$$\large{ D' }$$ = space diagonal $$\large{ in }$$ $$\large{ mm }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$

## Edge of a Right Rectangular Prism formulas

$$\large{ a = \frac { V } {b\;h } }$$

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

$$\large{ b = \frac { V } {a\;h } }$$

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

Symbol English Metric
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ D' }$$ = space diagonal $$\large{ in }$$ $$\large{ mm }$$
$$\large{ V }$$ = volume $$\large{ in^3 }$$ $$\large{ mm^3 }$$

## Height of a Right Rectangular Prism formulas

$$\large{ h = \frac { V } {a\;b } }$$

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

Symbol English Metric
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ D' }$$ = space diagonal $$\large{ in }$$ $$\large{ mm }$$
$$\large{ V }$$ = volume $$\large{ in^3 }$$ $$\large{ mm^3 }$$

## Surface Area of a Right Rectangular Prism formula

$$\large{ A_s = 2\; \left( a\;b + a\;h +b\;h \right) }$$
Symbol English Metric
$$\large{ A_s }$$ = surface area (bottom, top, sides) $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ h }$$ = height  $$\large{ in }$$  $$\large{ mm }$$

## Volume of a Right Rectangular Prism formula

$$\large{ V= a\;b\;h }$$
Symbol English Metric
$$\large{ V }$$ = volume $$\large{ in^3 }$$ $$\large{ mm^3 }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$

Tags: Volume Equations