Posted by **cindy** on Thursday, January 12, 2012 at 5:59pm.

Find the area of a regular pentagon with a side of 6 ft. Give the answer to the nearest tenth.

ok can't remember how to do this

- geometry -
**Reiny**, Thursday, January 12, 2012 at 6:31pm
A regular pentagon can be drawn as 5 conguent isosceles triangles with a central angle of 72° each, and equal base angles of 54°.

So just find the area of one of these by first finding the altitude of one of them

tan 54° = h/3

h = 3tan54°

area of one of them = (1/2)base x height

= (1/2)(6)(3tan54)

= 9tan 54°

so the whole pentagon = 45tan 54°

= appr. 61.9 square ft

- geometry -
**Shay**, Thursday, January 12, 2012 at 6:33pm
You forgot to give us the lenght of the side of the line that connects from the middle of the pentagon to a side of the pentagon.

- geometry -
**Steve**, Friday, January 13, 2012 at 12:00am
It's there; you just need to recognize it:

h = 3tan54°

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