Geometry

[Shamhoon]

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

[navami]

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

[Shamhoon]

thank you so much for the reply...

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

[navami]

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.

[Shamhoon]

thanks a ton!

very well explained:-)