What is the surface area of the right square pyramid if the height is 11.1 yards and the base is 5.3 yards?

Surface Area (S.A.) = Lateral area (L.A.) + Base Area (B)

Since the base of the pyramid is a square, then B = (5.3 yd)2 = 28.09 yd2.

To find L.A., the sum of the four triangular areas with base 5.3 yd, we need to find first their slant height (l) by using the Pythagorean theorem.

l = √[(5.3/2)2 + 11.12] = √(28.09/4 + 123.21) = √[(28.09 + 123.21*4)/4] = (√520.93)/2 yd.

L.A. = 4[(1/2)(5.3√520.93)] = 10.6√520.93 yd2.

S.A. = 10.6√520.93 + 28.09 ≈ 270 yd2.