The slant height of the hexagonal pyramid is: B. 14 inches.
Area of a regular hexagon = 3√3/2(s²)
First, find the area of the regular hexagon:
Area = 3√3/2(s²) = 3√3/2(10²) = 150√3 in.².
Surface area is given as 420 + 150√3 in.².
Area of the 6 triangles = surface area - area of hexagonal base = 420 + 150√3 - 150√3
Area of the 6 triangles = 420 in.²
Area of 1 triangle = 420/6 = 70 in.²
Use the area of a triangle to find the slant height (h):
70 = 1/2(10)(h)
2(70) = 10(h)
140/20 = h
h = 14 in.
The answer is B. 14 inches.
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