Question

Find the surface area of the regular pyramid shown to the nearest whole number.

Answer 1

First, we must understand what surface area means. This is the sum of all the areas of its lateral faces and its base. When we say lateral face, it means the triangles at the sides of the pyramid. 
The lateral surface area of the pyramid is given by the formula: LSA = 0.5PL, where P is the perimeter of the base, and L is the slant height.
LSA = 0.5(15 m)(6)(12 m) = 540 m²

We add the area of the base in order to get the total surface area:
Area of regular hexagon = (3√3)a²/2 = (3√3)(15 m)²/2 = 584.57 m²
TSA = 584.57 m² + 540 m²  = 1124.57 m² ≈ 1,125 m²