Given: regular tetrahedron V-ABC of edge 6 cm.?

Question

Compute:
a. slant height of face ABV
b. altitude Ov
c. area of the base
d. lateral area
e. total area

Answer 1

a) Slant height would be 3*sqrt(3) since it's a 30-60-90 triangle
b) Altitude would be 2*sqrt(6). You can make a triangel from the vertex of the top to a base. Then use the pythagorean theorem to do c^2-a^2=b^2.
c) Area of base is 9*sqrt(3)... Formula for equilateral triangle is sqrt(3)/4*s^2 where s is the side.
d) The lateral area is the surface area minus the base... so 27*sqrt(3)
e) The total area would be the surface area I'm guessing... So 4*9*sqrt(3)=36*sqrt(3)

Answer 2

a. 3√3 cm
b. √(27 - 3) = 2√6
c. 9√3 cm^2
d. 27√3
e. 36√3