A Church spire in a form of a regular hexagonal pyramid whose base edge is 8ft and whose altitude is 75ft is to be painted at a cost of 22 dollars per sq. yard. What is the total cost?

Given:

base edge - 8 ft

altitude or height - 75 ft

Surface area = [ (3√3) / 2] a² + 3a[√h² + (3a²/4) ]

S. A = 2.6*8² + 3 (8) * √75² + [ (3*8²) / 4]

S. A = 166.4 + 24 * √5625 + 48

S. A = 166.4 + 24 * √5674

S. A = 166.4 + 24 * 75.33

S. A = 166.4 + 1807.92

S. A = 1974.32 ft²

convert square feet to square yard.

1 sq ft = 0.1111 sq yd

1974.32 ft² * 0.1111 sq. yd/sq. ft = 219.35 sq yd.

22 per sq. yard

219.35 sq. yard * $22/sq. yd = $4,825.70

Total cost is $4,825.70