Question

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?

• A. 10² sq cm
• B. 12² sq cm
• C. 15² sq cm
• D. 20² sq cm

Answer 1

The correct option is B 12² sq cm

Altitude of the traingular faces = $\sqrt{\frac{a^2}{4}+9}$
Area of faces =2 x a x $\sqrt{\frac{a^2}{4}+9}$
The total surface area = area of base + lateral surface area
= a${}^2$ + 2 x a x $\sqrt{\frac{a^2}{4}+9}$
Lets us put a=8 (smallest value whch will yield an integer area, Area = 64 + 2 $\times$ 8 $\times$ 5 =144)

= 12${}^2$