Question

A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and circle. (Hint: remember Corollary 1-- the area of an equilateral triangle is 1/4(s^2)(sqrt 3).)

Answer 1

Area of a circle:
A c = r² π = 3² π = 9 π
9 π : 6 = 1.5 π ( area of the 1/6 of a circle )
Area of an equilateral triangle:
A t = 1/4 · s² · √3 = 1/4 · 3² √3 = 1/4 · 9 √3 = 2.25 √3
Area of a segment = 1.5 π - 2.25 √3 = 4.71 - 3.90 = 0.81.
Answer: The area of a segment is 0.81 squared inches.