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geometry intermediate

Problem

A regular hexagon is inscribed in a circle of radius

10

inches. Its area is:

(A)

150 s q r t (3) s q . in .

(B)

150 s q . in .

(C)

25 s q r t (3) s q . in .

(D)

600 s q . in .

Solution

Using the formula for the area of a hexagon given the circumradius:

\frac{3 3}{2 π} = \frac{A}{1 0 ^{2} π} ⟹ 100 \cdot 33 π = 2 A π ⟹ 50 \cdot 33 = A ⟹ 1503 1503 sq. in.

Final answer

A