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:

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: $$A= \dfrac{5 \cdot 4,33 }{2}$$

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

So, the area of the polygon is: $$A_{prism}=2\cdot 10,82 + 150 = 171,65$$

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

Generalizing,$$A_{lateral}= perimetre_{basis} \cdot height \\Area= 2 \ Area_{basis} +Area_{laterals} \\ Volume=Area_{ basis} \cdot height$$