Problem: A regular hexagon is inscribed in a circle of radius 101010 inches. Its area is:
Answer Choices:
A. 1503150 \sqrt{3}1503 sq. in. B. 150150150 sq . in. C. 25325 \sqrt{3}253 sq. in. D. 600600600 sq. in. E. 3003300 \sqrt{3}3003 sq. in.
Solution:
A=12ap=12⋅53⋅60=1503A=\dfrac{1}{2} a p=\dfrac{1}{2} \cdot 5 \sqrt{3} \cdot 60=150 \sqrt{3}A=21ap=21⋅53⋅60=1503 (square inches).