# Pentagon Inscribed In A Circle...

• Aug 26th 2008, 01:34 PM
topaz192
Pentagon Inscribed In A Circle...
Ok. I know how to find the area of, like, a pentagon. But in this problem is wants me to find the area of the courthouse....like outside the pentagon.

So on a problem like this, do I follow through with steps to find the area of a pentagon and go from there?

Question:

The center of the pentagon in VA is a courtyard in the shape of a regular pentagon. The pentagon would be inscribed in a circle with radius of 300 ft. Find the area of the courtyard.

http://i20.photobucket.com/albums/b2...188/matttt.jpg

I drew the pentagon. :]

What would I do for the next step?
• Aug 26th 2008, 01:42 PM
Moo
Hi again !
Quote:

Originally Posted by topaz192
Ok. I know how to find the area of, like, a pentagon. But in this problem is wants me to find the area of the courthouse....like outside the pentagon.

So on a problem like this, do I follow through with steps to find the area of a pentagon and go from there?

Question:

The center of the pentagon in VA is a courtyard in the shape of a regular pentagon. The pentagon would be inscribed in a circle with radius of 300 ft. Find the area of the courtyard.

http://i20.photobucket.com/albums/b2...188/matttt.jpg

I drew the pentagon. :]

What would I do for the next step?

The next step will be to change your sketch (Rofl)

If the pentagon is inscribed in a circle, it means that the circle is all around the pentagon. Here, the circle is inscribed in the pentagon, this is very different ! :)

Here is a sketch :
Attachment 7591

The pentagon is inscribed in the green circle. In order to calculate the area of the pentagon, imagine it can be divided into 5 isosceles triangles (summit is the center).
• Aug 26th 2008, 01:49 PM
topaz192
(Giggle) Whoopsiiee! Lol

So 360 / 5 = 72 degrees.

1 / 2 (300?) ^2 sin72 = ____ times 5 sides = ________

• Aug 26th 2008, 01:50 PM
Moo
Quote:

Originally Posted by topaz192
(Giggle) Whoopsiiee! Lol

So 360 / 5 = 72 degrees.

1 / 2 (300?) ^2 sin72 = ____ times 5 sides = ________