Answer to Question #148819 in Geometry for anlp

Question

The total area of a regular tetrahedron is 110.85 m2, determine its base edge in m.

Answer 1

Using the formula

$Area(A)=\sqrt3\times a^2$

where $a$ is the length of the side and making $a$ the subject of the formula, we obtain:

$a=\frac{1}{3}\times3^{\frac{3}{4}}\times\sqrt A$

Substituting for A,

$a=\frac{1}{3}\times3^{\frac{3}{4}}\times\sqrt{ 110.85}$

therefore:

$a=7.99995m$

Which is approximately $a= 8m$