SA of a regular tetrahedron

May 2010
5
1
A regular tetrahedron is a triangular
pyramid. What is the total surface
area of a regular tetrahedron with​
base edges of 7 cm?

I started by using
1/2 × Perimeter × [Side Length] + [Base Area]
(1/2) (21) (?) + (sqrt(36.75))

So im not sure if this is the correct forumula or if the numbers i used to plug in are correct.
 

Opalg

MHF Hall of Honor
Aug 2007
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Leeds, UK
The tetrahedron has four faces, each of which is an equilateral triangle with sides 7 cm. So your answer should be 4 times the area of that triangle.

The area of the triangle is half the base, times the vertical height which in this case is \(\displaystyle 7\sin60^\circ = 7\sqrt3/2\).

Put all that information together and you'll get the answer.