All five faces of a regular pyramid with a square base are found to be of the same area. The height of the pyramid is 3 cm. What is the minimum total area (integral) of all its surfaces?
Altitude of the traingular faces = √a24+9
Area of faces =2 x a x √a24+9
The total surface area = area of base + lateral surface area
= a2 + 2 x a x √a24+9
Lets us put a=8 (smallest value whch will yield an integer area, Area = 64 + 2 × 8 × 5 =144)