## find the area of a square inscribed in a circle

Geometric formulae, word problems, theorems and proofs, etc.
mdspham
Posts: 1
Joined: Thu Apr 16, 2015 3:30 am
Contact:

### find the area of a square inscribed in a circle

Hi all, please help me with this problem: find the area of a square if it is inscribed in a circle in which one arc intercepted by a side of the square has length 12pi. Thanks for all the help.

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### Re: find the area of a square inscribed in a circle

find the area of a square if it is inscribed in a circle in which one arc intercepted by a side of the square has length 12pi.
Draw the square. Draw the circle inside. Draw horizontal and vertical lines through the center that split the square into four equal smaller squares. Label one of the smaller squares' arc with "12pi".

The smaller square with the labeled arc is a sector of the circle. What is the size of the angle for this sector? With the arc length they gave you and the central angle you know, what is the radius? This is half the length of a side of the big square. What is the whole length? What is the area?