An octahedron is really just two identical pyramids with their bases taped together.
SA ≈ 560 in2
Find the surface area of the solid.
The four identical pyramids' lateral area, the faces of the prism, and the base of the prism are all included in the surface area.
SA ≈ 3425 m2
Rabbi Schwartz noticed that the net of a regular hexagonal pyramid made a shape similar to the Star of David, so he decided to build a synagogue in that shape. If he wants to paint the building light blue, how much area will he cover?
In this case, "area" means, "lateral area." You didn't think he was going to paint the ground, did you? Oy vey!
Rabbi Schwartz will have to paint about 4680 ft2 of synagogue. Or get the kids at Hebrew school to do it.