Find the radius of a circle around a regular triangle whose area is 3√3.
August 30, 2021 | education|
Since, by condition, triangle ABC is regular, all its internal angles are equal to 60.
Then the area of the triangle ABC is equal to:
Saavs = AB * BC * Sin60 / 2 = AB2 * Sin60 / 2.
AB2 = 2 * Savs / Sin60 = 2 * 3 * √3 / (√3 / 2) = 12.
AB = √12 = 2 * √3 cm.
The radius of the circumscribed circle about a regular triangle is:
R = AB / √3 = 2 * √3 / √3 = 2 cm.
Answer: The radius of the circumscribed circle is 2 cm.
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