# Thread: Pentagon Inscribed In A Circle...

1. ## 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.

I drew the pentagon. :]

What would I do for the next step?

2. Hi again !
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.

I drew the pentagon. :]

What would I do for the next step?
The next step will be to change your sketch

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 :

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).

3. Whoopsiiee! Lol

So 360 / 5 = 72 degrees.

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

4. Originally Posted by topaz192
Whoopsiiee! Lol

So 360 / 5 = 72 degrees.

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