Alan G. answered • 03/02/16
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When a pentagon is inscribed in a circle, the segments drawn from the center of the circle to the five vertices will form five congruent isosceles triangles. I am assuming the pentagon is regular (has five equal sides). Please let me know if this is not part of the problem. Each isosceles triangle has a central angle of 360/5 = 72°. Since the two adjacent sides have length 20 cm, all you must do is find the area of one of these triangles and multiply it by 5 to get the final answer.
The formula A = ½ ab sin C can be used, where a and b are the two sides and C is the included angle.
With the information you have given (and my assumption), the area of one triangle is A = 50 sin 72° ≈ 47.55 cm2. After multiplying by 5, you obtain the pentagon's area as 237.8 cm2.
