# SAT Geometry Question

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• Jul 17th 2013, 07:53 AM
anthonybjj94
SAT Geometry Question
Attachment 28845

The part that is cut off is asking the area of the shaded section of the circle. How do I solve this problem only knowing one side of the square?
• Jul 17th 2013, 08:02 AM
MINOANMAN
Re: SAT Geometry Question
there is a problem with your post
I can't see the problem....
• Jul 17th 2013, 08:07 AM
anthonybjj94
Re: SAT Geometry Question
Thank you. I will try to remedy this.
• Jul 17th 2013, 08:09 AM
anthonybjj94
Re: SAT Geometry Question
I updated the post.
• Jul 17th 2013, 08:34 AM
Plato
Re: SAT Geometry Question
Quote:

Originally Posted by anthonybjj94
Attachment 28845
The part that is cut off is asking the area of the shaded section of the circle. How do I solve this problem only knowing one side of the square?

The radius of that circle is 1. The angle at O is $\displaystyle \tfrac{\pi}{2}$.
Thus the shaded area is $\displaystyle \tfrac{1}{4}$ the area of the circle.
• Jul 17th 2013, 08:38 AM
anthonybjj94
Re: SAT Geometry Question
I understand that the radius is 1, due to the side of the square being the diameter. However, I don't understand how you found O's angle. Can you explain, please?
• Jul 17th 2013, 09:11 AM
Plato
Re: SAT Geometry Question
Quote:

Originally Posted by anthonybjj94
I don't understand how you found O's angle. Can you explain, please?

You are expected to know about the diagonals of a square.
What are the properties of diagonals?
• Jul 17th 2013, 09:18 AM
anthonybjj94
Re: SAT Geometry Question
They are perpendicular, correct?
• Jul 17th 2013, 09:20 AM
anthonybjj94
Re: SAT Geometry Question
and, I believe, make four 45-45-90 triangles, which would mean that the shaded area is 1/4 of the circle.
• Jul 17th 2013, 09:23 AM
anthonybjj94
Re: SAT Geometry Question
A=Pi(D)

A=Pi(2)/4

A= Pi/2

I think I got it!
• Jul 17th 2013, 09:32 AM
anthonybjj94
Re: SAT Geometry Question
But I do have an additional question:

When I plugged in the radius to the formula A=Pi(r)2 I received Pi/4 as an answer. Where did I err?
• Jul 17th 2013, 12:53 PM
topsquark
Re: SAT Geometry Question
Quote:

Originally Posted by anthonybjj94
A=Pi(D)

A=Pi(2)/4

A= Pi/2

I think I got it!

This is where your error is: $\displaystyle C = \pi D$, not A.

-Dan
• Jul 17th 2013, 02:51 PM
anthonybjj94
Re: SAT Geometry Question
Silly me. As you can see, I am still knocking the rust off. Thank you for all of the help! What you do is admirable!