What is the surface area of this square pyramid?
The base is a square; therefore, its area is 4.62 = 21.16.
Since the left-hand triangle of the front sides is a 30-60-90 triangle, the dashed line segment has a value equal to
sqr(3) x the base of the left-hand triangle (the distance from the corner dot to the middle dot). Since the distance from the corner dot to the middle dot = 1/2 x 4.6 = 2.3, the length of the dashed line segment = 2.3 x sqrt(3).
The area of the front triangle = 1/2 x base x height = 1/2 x (4.6) x (2.3 x sqrt(3)) = 9.1625.
The total surface area = (area of the base) + 4 x (area of the front triangle) = 21.16 + 4 x (9.1625) = 57.81 square yds.