# Right Pentagonal Prism

Written by Jerry Ratzlaff on . Posted in Solid Geometry

• Right pentagonal prism (a three-dimensional figure) has pentagonal bases and each face is a regular polygon with equal sides and equal angles.
• 20 base diagonals
• 10 face diagonals
• 20 space diagonals
• 2 bases
• 15 edges
• 5 side faces
• 10 vertexs

### Base Area of a Right Pentagonal Prism formula

$$\large{ A_b= \frac {1}{4}\; \sqrt { 5 \left( 5+2\; \sqrt {5} \right) a^2 } }$$

Where:

$$\large{ A_b }$$ = base area

$$\large{ a }$$ = edge

### Edge of a Right Pentagonal Prism formula

$$\large{ a = 25^{3/4} {\frac {\sqrt {A_b} } { 5\; \left( \sqrt {20}\; +5 \right) ^1/4 } } }$$

$$\large{ a = \frac { - \left ( 5\; \sqrt {5} h - \sqrt { 125\;h^2 + 10\; A_s\; \sqrt { \sqrt {500}\; +25 } } \right) } { 5\; \sqrt { \sqrt { 20 }\; +5 } } }$$

$$\large{ a = \frac {A_l} {5\;h} }$$

Where:

$$\large{ a }$$ = edge

$$\large{ A_b }$$ = base area

$$\large{ h }$$ = height

$$\large{ A_l }$$ = lateral surface area

$$\large{ A_s }$$ = surface area

### Height of a Right Pentagonal Prism formula

$$\large{ h = \frac {A_s} {5\;a} - \frac {1}{10}\;a\; \sqrt { \sqrt {500} +25 } }$$

Where:

$$\large{ h }$$ = height

$$\large{ a }$$ = edge

$$\large{ A_s }$$ = surface area

### Lateral Surface Area of a Right Pentagonal Prism formula

$$\large{ A_l = 5\;a\;h }$$

Where:

$$\large{ A_l }$$ = lateral surface area

$$\large{ a }$$ = edge

$$\large{ h }$$ = height

### Surface Area of a Right Pentagonal Prism formula

$$\large{ A_s = 5\;a\;h + \frac {1}{2} \; \sqrt { 5\; \left ( 5+2 \;\sqrt {5} \right) }\; a^2 }$$

Where:

$$\large{ A_s }$$ = surface area

$$\large{ a }$$ = edge

$$\large{ h }$$ = height

### Volume of a Right Pentagonal Prism formula

$$\large{ V= \frac {1}{4} \; \sqrt { 5\; \left ( 5+2\; \sqrt {5} \right) } \;a^2\;h }$$

Where:

$$\large{ V }$$ = volume

$$\large{ a }$$ = edge

$$\large{ h }$$ = height

Tags: Equations for Volume