The prism: Surface area and volume

The prism is a polyhedron composed by two bases that can be any polygons joined by parallelograms. In a certain way, we can say that, to create a prism, it is necessary to accumulate many equal polygons.

The regular prisms take regular polygons as bases. For example, the following figure is a prism with pentagons for bases:

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Example

Calculate the area and volume of a prism of a height of $10 m$ and with an equilateral triangle as side $5 m$ for bases.

The area of the triangle is: $A = \frac{5 \cdot 4, 33}{2}$

The side area has a value of: $3 \cdot 5 \cdot 10 = 150$

So, the area of the polygon is: $A_{p r i s m} = 2 \cdot 10, 82 + 150 = 171, 65$

And the volume $V = 10 \cdot 10, 82 = 108, 3$

Generalizing, $A_{l a t e r a l} = p e r i m e t r e_{b a s i s} \cdot h e i g h t A r e a = 2 A r e a_{b a s i s} + A r e a_{l a t e r a l s} V o l u m e = A r e a_{b a s i s} \cdot h e i g h t$