# Right Square Prism

on . Posted in Solid Geometry

• Right square prism (a three-dimensional figure) has square bases, four faces that are rectangles with equal sides and equal angles.
• Diagonal is a line from one vertices to another that is non adjacent.
• 1 base
• 12 edges
• 5 faces
• 8 vertexs
• 2 base diagonals
• 10 face diagonals
• 4 space diagonals ## Base Area of a Right Square Prism formula

$$\large{ A_b = a^2 }$$
Symbol English Metric
$$\large{ A_b }$$ = base area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$ ## Diagonal of a Right Square Prism formula

$$\large{ D' = \sqrt {2\;a^2 + h^2} }$$
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 Square Prism formulas

$$\large{ a = \frac {1} {2} \; \sqrt {2\;D'^2 + 2\;h^2} }$$

$$\large{ a = \frac {1} {2} \; \sqrt {4\;h^2 + 2\;A_s}\; -h }$$

$$\large{ a = \sqrt { \frac {V} {h} } }$$

Symbol English Metric
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ D' }$$ = space diagonal $$\large{ in }$$ $$\large{ mm }$$
$$\large{ A_s }$$ = surface area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ V }$$ = volume $$\large{ in^3 }$$ $$\large{ mm^3 }$$ ## Height of a Right Square Prism formulas

$$\large{ h = \frac {A_s} {4\;a} - \frac {a} {2} }$$

$$\large{ h = \sqrt {D'^2 + 2\;a^2} }$$

Symbol English Metric
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ D' }$$ = space diagonal $$\large{ in }$$ $$\large{ mm }$$
$$\large{ A_s }$$ = surface area $$\large{ in^2 }$$ $$\large{ mm^2 }$$ ## Surface Area of a Right Square Prism formula

$$\large{ A_s= 2\;a^2 + 4\;a\;h }$$
Symbol English Metric
$$\large{ A_s }$$ = surface area (bottom, top, sides) $$\large{ in^2 }$$  $$\large{ mm^2 }$$
$$\large{ a }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$ ## Volume of a Right Square Prism formula

$$\large{ V=a^2\;h }$$
Symbol English Metric
$$\large{ V }$$ = volume $$\large{ in }$$ $$\large{ mm }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$ 