Surface Area & Volume

Welcome to our dodecahedron calculator! A dodecahedron is a three-dimensional solid figure with 12 flat faces. It is one of the five Platonic solids, which are regular polyhedra. 
In this calculation, we will use basic geometry principles to find the surface area and volume of a dodecahedron. 
CalculationInput
﻿﻿a
:5m​
﻿
ExplanationTo do this, we will use the length of each of the dodecahedron's edges to calculate the area of each face. 
Once the area of each face is known, we can calculate the total surface area and volume of the dodecahedron.
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Surface area and volume of a dodecahedron
Surface Area
To calculate the surface area of a dodecahedron, you will need to use the formula:
﻿
A=325+105a2A = 3\sqrt{25 + 10\sqrt{5}}a^2A=325+105​​a2
﻿﻿A
:516.1m2​
﻿
Volume
To calculate the volume of a dodecahedron, you will need to use the formula:
﻿
V=15+754a3V = \frac{15 + 7\sqrt{5}}{4}a^3V=415+75​​a3
﻿﻿V
:957.9m3​
﻿
Where: 
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a=Length of one sidea=Length \: of \: one \: sidea=Lengthofoneside
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Dodecahedron: Surface Area & Volume

Calculation

Input

Explanation
