Supermaverick wrote:
ABCDEF is a regular hexagon inscribed inside a circle. If the shortest diagonal of the hexagon is of length 3 units, what is the area of the shaded region.
1) 1/6(3Π − (9√3)/2)
2) 1/6(2Π − (6√3)/2)
3) 1/6(3Π − (8√3)/2)
4) 1/6(6Π − (15√3)/2)
5) 1/6(6Π − (13√3)/2)
Attachment:
reg.hex-in-circle.jpg [ 105.54 KiB | Viewed 5180 times ]
Answer A. From the figures, just a few things to note:
1. Short diagonal BD = 3 is also the side opposite a 30-60-90 triangle created by bisection of regular hexagon's 120 degree angle
2. I used that side to figure side AB, which is also radius. (I got that they're equal; just draw imaginary line from my figure's center to B . . . just thought I ought to keep the diagram as simple as possible.)
3. I didn't show calculations, and assumed some things would be obvious, e.g. diameter AD = 2r. I did show formulas and values. The math isn't hard. Just
painstaking. I think I'm shell-shocked.
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