Math CentralQuandaries & Queries


Question from Sandra, a parent:

Hi , my 8th grade daughter has this word problem on her worksheet.

If the area of a regular pentagon is A=1.720a^2, in which a is one of the sides. Find the area of a regular pentagon with a side that measures 50cm.

Hi Sandra,

The area of a regular pentagon with side length a centimeters is A = 1.720 a2 square centimeters. This is a mathematical shorthand (algebraic) way of saying something that would be cumbersome to write out in prose.

If you know the length of a side of a regular pentagon in centimeters then to find the area of the pentagon in square centimeter you multiply the side length by the side length, and then multiply the result by 1.720.

The algebraic expression is certainly more compact.

For example, suppose I have a regular pentagon and the side length is 15 cm. In the area expression A = 1.720 a2 the side length is represented by a. Thus in my pentagon a = 15 cm so the area is

A = 1.720 a2 = A = 1.720 × 152 = 1.720 × 225 = 387 square centimeters.

I hope this helps,


A formula is simply a list of instructions. Your formula tells you to take the side of your pentagon, then square that number, then multiply the resulting square number by 1.720. This final number is the desired area. (Or, more correctly, it is the desired area accurate to about three decimal places.)


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