Calculate The Surface Area Of A Dodecahedron

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Tetrahedron

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Dodecahedron

Icosahedron

The surface area of a dodecahedron refers to the total area of all the faces of this polyhedron, which is a three-dimensional shape with 12 regular pentagonal faces. This shape is commonly used in architecture and design, especially in decorative applications, due to its unique and aesthetically pleasing geometry.

In real-life constructions, the dodecahedron can be seen in various forms of architectural ornamentation such as doorknobs, light fixtures, and sculptures. It has also been used in the design of various sports balls, including soccer balls and golf balls.

Knowing the surface area of a dodecahedron can be useful in determining the amount of material needed to construct a particular object or in calculating the cost of materials. Additionally, understanding the surface area can aid in the creation of accurate blueprints and design plans.

The formula for determining the surface area of a dodecahedron is defined as:

\(SA\) \(=\) \(3\) \(\cdot\) \(\sqrt{25 + 10 \cdot \sqrt{5}}\) \(\cdot\) \(a^2\)

\(SA\): the surface area of the dodecahedron

\(a\): the length of any side

The SI unit of surface area is: \(square \text{ } meter\text{ }(m^2)\)

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