What’s the Surface Area and Volume formula for an equilateral triangular prism

Question

Pls help me. I’m in ap calculus and I need the equations

Answer 1

Let the triangle be of side length s and a height h.

Then, to derive the area of the triangle: bisect a side; then, for one of the triangles created, one side is of length 1/2 s and the hypotenuse is of length s, so the other side of the triangle is of length 1/2 s sqrt(3)

Then, we see that the altitude of the original triangle is 1/2 s sqrt(3). Thus, the area of the triangle is 1/2 bh = 1/2 s (1/2 s sqrt(3)) = sqrt(3)/4 s^2

Then, the volume of the prism is sqrt(3)/4 s^2 h