#$&*
Mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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For Assignment 3: Question R.3.40_ shows a circle with a rectangular square inside it. The shaded region is the area between the square and the circle's perimeter. The square has a base of 2 and an altitude of 2. The question states, Find the area of the shaded region. I have looked in the book, watched the videos for this section, and have not found an example of this type of problem.
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I understand that I need to figure out what the area between the circle's perimeter and the square's four sides is. What I am rusty on is how to go about this. I know I need to figure out the area of the circle, subtract the area of the square (4) from that figure to find the area of the shaded region. So far I have this:
A of square = 2 * 2 = 4
A of Circ. = pi r^2 = pi (x + 2)^2 = 4x^2pi units^2 ??????
A of shaded region = (pi r^2) - 4
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What is the formula that I would use to figure this problem out?
@& Good question. You're definitely on the right track.
I believe you will understand that the diagonal of the square is equal to the diameter of the circle, since the corners of the square are on the circle and a diagonal will pass through their common center.
If the side of the square is x, then a diagonal divides it into two right triangles, with the diagonal as the hypotenuse. What are the legs of such a triangle, in terms of x, and what therefore is the expression for the diagonal?
The length of the diagonal is the diameter of the circle, so by setting the two equal you get an equation you can solve for x.
See what you can do with this. If this doesn't lead you to a solution, you're welcome to submit a copy of this, including my message, and insert any additional work you've been able to do, and additional questions if you have them.*@