The radius of the circle is 6. Find the area of a regular triangle inscribed in this circle.

univerkov | January 12, 2021 | education

Since the inscribed triangle is regular, all of its interior angles are 60.
Then the radius of the circumscribed circle is: R = a / 2 * Sin60.
a = 2 * 6 * √3 / 2 = 6 * √3 cm.
Then Str = a2 * Sin60 / 2 = 108 * √3 / 4 = 27 * √3 cm2.
Answer: The area of the triangle is 27 * √3 cm2.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.