Help with math? Please!

This image shows a square pyramid.

What is the surface area of this square pyramid?

36 ft²
72 ft²
78 ft²
84 ft²

1 Answer
Mar 27, 2018

36 #ft^2#


surface area is lateral
a perpendicular line from the top angle to the bottom is a perpendicular bisector so the line is now 3 and 3
so in triangle one (as i named it) we have a isosceles triangle (45-45-90) or a special right triangle (x-x-x#sqrt#2).
the area of triangle one is #1/2*bh# , so #1/2*3*3#, i.e. #9/2#
#9/2#area of one triangle, as the base is a square all the measures are same so the area of all triangles will be same. on each side we have 2 triangles and we have 4 side so 8 triangles.
the total suface area is #(9/2*8) = 36#
enter image source here