Quandaries
and Queries 

Who is asking: Parent Level: Middle Question: 

Hi, The shape you are describing is called a regular octagon. I drew in the diagonals to show the eight triangles. Here is one of them which I labeled CAB. I also drew a line from C to the midpoint M of AB.
As you noted CA = BC = 6 feet. The angle BCA is one eighth of 360^{o} so angle BCA is 45^{o}. The angles CAB abd CBA have the same angle measurement since the triangle CAB is isosceles. The three angles in a triangle add to 180^{o} angle CAB has angle measurement
To completely describe the triangle all that remains is to find the length of the side AB. For this I need to use trigonometry. The cosine of the angle CAM is AM/CA and hence
Since AM is half of AB,
which is approximately 4 feet 7 ^{1}/_{8} inches. Penny 

