1. ## SAT Geometry Question

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?

2. ## Re: SAT Geometry Question

there is a problem with your post
I can't see the problem....

3. ## Re: SAT Geometry Question

Thank you. I will try to remedy this.

4. ## Re: SAT Geometry Question

I updated the post.

5. ## Re: SAT Geometry Question

Originally Posted by anthonybjj94

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.

6. ## 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?

7. ## Re: SAT Geometry Question

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?

8. ## Re: SAT Geometry Question

They are perpendicular, correct?

9. ## 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.

10. ## Re: SAT Geometry Question

A=Pi(D)

A=Pi(2)/4

A= Pi/2

I think I got it!

11. ## 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?

12. ## Re: SAT Geometry Question

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

13. ## 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!