Area of a hexagon

Geometry Level pending

An equilateral triangle ABC is inscribed in a circle of some radius. Points D, E and F are the midpoints of minor arcs BC, AC and AB respectively. If AD = 16cm, find the area of the hexagon AFBDCE.


The answer is 166.277.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

arc AB = 1/3 of the circumference, so is arc BC. arc BD = arc DC = 1/6 of the circumference (midpoint given). so, arc AD = 1/3 of circumference + 1/6 of the circumference = 1/2 of circumference so, AD is diameter. so r = 8 cm. then use centroid theorem, trig and other stuff.

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Given that the radius is 8, the area of this regular hexagon is 6 × 1 2 × 8 × 8 × 3 2 ≈ 166.277 6 \times \frac{1}{2} \times 8 \times 8 \times \frac{ \sqrt{3} } { 2} \approx 166.277 .

I have updated the answer accordingly.

Calvin Lin Staff - 6 years, 6 months ago

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