In a regular 3-angled pyramid, the side rib = 8 cm, and the angle of the rib to the base plane = 60 degrees.

In a regular 3-angled pyramid, the side rib = 8 cm, and the angle of the rib to the base plane = 60 degrees. Find the surface area of the pyramid.

We first find out the area of the base. If the angle between the lateral face and the base is 60 degrees, and the lateral face itself is 8, then half of the base will be equal to the cosine of the lateral face at a known angle, i.e. half of the side of the base 4 => the whole of the side of 8. So the sides and bases are the same triangles. The area of the lateral side is 1 / 2ab, those 1/2 • 8 • 4 = 16, and we have 4 such triangles.
Answer 64