Problem Solving

A pyramid with four equal-sized flat surfaces and a base of 36 feet (square) has a height of 10 feet. What is the total

surface area of the pyramid, excluding the base?

A . 12 root of 31

B. 12 root of 109

C. 24 root of 31

D. 24 root of 109

E. 48 root of 31

IMO B.

from base area, we can calculate the base sides,
for a square area36, each side: a=square root of 36=6

Consider the right triangle where, base=6/2=3 and height given=10,
then by Pythagoras theorem hypotnuse= square root of (10^2 + 3^2) = square root of 109

now surface area of each side( triangle) = (1/2)*base*height = (1/2)*6*square root of 109

since there are four sides, hence total surface area= 4*(1/2)*6*square root of 109 = Option B

thank you so much for the reply...

But why are we not taking 10 as the height ???

Pyramid is slant, the height (10) given in the problem is the distance between the pyramid's topmost point to the ground.
so to calculate the surface area u need the slant height of each of the triangles (each of the four sides), which can be calculated from Pythagorean theorem.

Please Ref to the attached diagram.

thanks a ton!

very well explained:-)