Question

Find the volume of a right prism with height h=10 cm, The base is equilateral triangle with side 4 cm, base altitude of ≈ 3.5 cm.

Answer 1

Answer:

$\boxed{V=40\sqrt{3}cm^3}$

Step-by-step explanation:

A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. In a right prism every edge that connects the base and the opposite face makes right angles with both faces. Moreover, a triangular prism is a solid whose base is a triangle. In general, a prism's volume is always equal to the area of its base, which has the same area of the top face, times its height. In mathematical language:

$V=A_{b}\times H \\ \\ Where: \\ \\ A_{b}:Base \ Area \\ \\ H:Height$

Since the base is an equilateral triangle with side 4 cm, then we'll use Heron's formula to find the area. This formula uses triangle's side lengths and the semiperimeter. A polygon's semiperimeter s is half its perimeter. So the area of a triangle can be found by $A=\sqrt{s(s-a)(s-b)(s-c)}$ being $a,\:b\:and\:c$ the corresponding sides of the triangle. So:

$s=\frac{4+4+4}{2}=6cm \\ \\ a=b=c=4cm \\ \\ A_{b}=\sqrt{6(6-4)^3}=4\sqrt{3}cm^2$

Finally:

$V=4\sqrt{3}\times 10 \\ \\ \boxed{V=40\sqrt{3}cm^3}$