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25 votes
25 votes
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.

User Clerenz
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1 Answer

28 votes
28 votes

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}

User Blankabout
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