Heathy builds a paper model of a regular tetrahedron, a pyramid with an equilateral triangle for the base and three equilateral triangles for the lateral faces. One of the faces of the tetrahedron has an area of 17 sq. inches. What is the total surface area of the tetrahedron?

Question

directrix · Answer

The four faces of a regular tetrahedron are congruent equilateral triangles. 
Congruent triangles have the same area.
If one of the triangles has area 17, then the surface area of the tetrahedron is 4*17 = 68 square inches.

anonymous · Answer

The base is an equilateral triangle, so use the area of that triangle first.

Since the other sides of the pyramid are ALSO equilateral triangles, they also have sides the same as your base and their areas are also 17, 17, 17! And thus have the same area you just calculated for the base!

So the total surface area is 4*17!