Question 1165477: The side of a regular pentagon is 25 cm. If the radius of its inscribed circle is 15 cm, find the area of the pentagon.
a. 937.5 cm2 b. 784.6 cm2
c. 825.75 cm2 d. 857.65 cm2
Found 3 solutions by Boreal, Alan3354, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The circle hits the sides and itself has area of πr^2=225 π or 706.86 cm^2
Draw this and note the 10 triangles that may be made. We know that because the central angle of each of those is 36 degrees and 360/36=10.
They are 36 degrees, because the internal angles of the pentagon are each 108 degrees {(n-2)/n}*180, and the line from the center to the vertex of each angle bisects it, so that is where 54 degrees comes from.
The area of each triangle is (1/2) bh with base 12.5 (half the side's length) and height 15 (the radius), so each triangle has area 93.75 cm^2. There are 10 of them, and the total area is 937.5 cm^2
A
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! The side of a regular pentagon is 25 cm. If the radius of its inscribed circle is 15 cm, find the area of the pentagon.
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 where n = # of sides and s = length of sides
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The area of the pentagon is not affected by the circle.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
If the radius of the inscribed circle into the regular pentagon is 15 centimeters, then its side CAN NOT be 25 centimeters.
The problem is a FAKE and is self-contradictory.
Such a pentagon DOES NOT EXIST.
Thanks to god, at this forum still there are tutors who know Math.
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