Find the length of a circle circumscribed about a regular hexagon with an area of 24√3cm2.
| September 1, 2021 | education
1. Determine the side a of the hexagon.
S = (3√3 * a ^ 2) / 2 = 24√3;
a ^ 2 = 2 * 24√3 / 3√3;
a = √16;
a = 4 cm.
The radius r of a circle circumscribed about a regular hexagon is equal to the side a of the hexagon.
r = a = 4 cm.
2. Determine the length of the circumscribed circle.
C = 2πr = 2 * 3.14 * 4 = 25.12 cm.
Answer: the length of the circumscribed circle is 25.12 cm.
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