Question

n 2008, the Queen Sesheshet Pyramid was discovered in Egypt. Archeologists determined that the original height of this right square pyramid was about 14 m and the original base side length was about 22 m. Determine its original lateral area to the nearest square metre.

Answer 1

you need to make a draw of the problem to understand what to do.
The height of the pyramid, and half the original base side length make a rectangle triangle, whose hypothenuse is the height of the lateral area of one of the pyramids faces, so we have. So we use Pythagoras:
hyp^2 = 11^2 + 14^2 = 317
hyp = 17.8 m
that is the height of the lateral area triangle

Now to find the area of the lateral area triangle, we have:
a = base*height/2 = 22*17.8/2
a = 195.8 m^2
that is the lateral area of the pyramid, 196 m^2