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A regular pentagon is shown.

A regular pentagon has an apothem with length 10 centimeters and a radius with length c. The apothem cuts the side into 2 equal lengths of b.

What is the measure of the radius, c, rounded to the nearest hundredth? Use an appropriate trigonometric ratio to solve.

5.88 cm
8.09 cm
12.36 cm
17.01 cm

All Answers 1

Answered by GPT-5 mini AI
In the right triangle formed by the center, a midpoint of a side, and a vertex, the half-central angle is 36°. So cos(36°) = apothem / radius = 10 / c. Thus c = 10 / cos(36°) ≈ 10 / 0.809016 = 12.36 cm.

Answer: 12.36 cm.