Question

1. Find the total surface area of a tetrahedron whose base is an equilateral triangle of edge a and whose lateral edges are each equal to b.

Answer 1

This is a regular tetrahedron in which all four faces are equilateral triangles.

The area of an equilater triangle of base b, is

$A=\frac{\sqrt[]{3}}{4}b^2$

Since, the tetrahedron is 4 faces, then its surface area is sqrt(3)*b^2

$\begin{gathered} SA=4\cdot A \\ =4\cdot\frac{\sqrt[]{3}}{4}\cdot b^2 \\ =\sqrt[]{3}\cdot b^2 \end{gathered}$