Question

The pentagonal area is 20 cm square. Point A located in the pentagon and equidistant from all sides of the pentagon about 5 cm. What is the perimeter of the pentagons.

Answer 1

Answer:

  about 8 cm

Step-by-step explanation:

The formula for the area of a regular polygon is ...

  A = 1/2Pa . . . . where P is the perimeter and "a" is the apothem, the distance from the center to a side

Filling in your numbers, we have ...

  20 cm^2 = (1/2)P(5 cm)

Dividing by the coefficient of P, we find ...

  2×(20 cm^2)/(5 cm) = P = 8 cm

The perimeter of the pentagon is about 8 cm.

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Comment on the problem

This calculation makes use of the area formula, as apparently intended. A regular pentagon with an apothem of about 5 cm will have an area of about 90.8 cm^2. The given geometry is impossible, as the pentagon is nearly 10 cm across. It cannot have a perimeter of only 8 cm.