Why is the formula for finding the area of a regular pentagon side squared times 1.72?

Why is it side squared times 1.72 is the formula for finding the area of a regular pentagon?

Coorect girl!

Area of a regular pentagon = 1.72048 x side (squared)

This is the easier one where the length of the side is given! However, there is another formula that can be used.

The area of a pentagon is given by:
Area = (½)x(apothem)x(perimeter)

Perimeter = 5 x side
Apothem = radius of incribed circle (of the pentagon)

Such a formula is used to find the apothem, because from the perimeter, you can always find the side of the pentagon.
Enjoy!

This entry was posted on Sunday, January 24th, 2010 at 2:47 am and is filed under area formula. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

3 Responses to “Why is the formula for finding the area of a regular pentagon side squared times 1.72?”

Alex on January 24th, 2010 at 8:13 am

It is basically the way the formula can be simplified.

See: http://mathforum.org/library/drmath/view/55311.html

Hopefully that can explain it for you!!!
References :
Maverick on January 24th, 2010 at 8:53 am

Coorect girl!

Area of a regular pentagon = 1.72048 x side (squared)

This is the easier one where the length of the side is given! However, there is another formula that can be used.

The area of a pentagon is given by:
Area = (½)x(apothem)x(perimeter)

Perimeter = 5 x side
Apothem = radius of incribed circle (of the pentagon)

Such a formula is used to find the apothem, because from the perimeter, you can always find the side of the pentagon.
Enjoy!
References :
nathan m on January 24th, 2010 at 9:40 am

u in geo? cuz im having that same problem and have geo finals next week and need to study my butt off. it is 1/2 x apothem x perimeter (of the figure).
References :

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