My Math Forum Area enclosed by a semi-circle and a quarter circle

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May 23rd, 2012, 09:16 PM   #1
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Area enclosed by a semi-circle and a quarter circle

Find the shaded area, which is enclosed by a square, semi-circle and a quarter of circle.

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 May 25th, 2012, 08:57 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,931 Thanks: 1125 Math Focus: Elementary mathematics and beyond Re: Area enclosed by a semi-circle and a quarter circle Using degree measure for angles, $\pi$$\frac{49}{4}$$\frac{\cos^{\small{-1}}(-.6)}{360}\,-\,\frac{49}{2}\,+\,\pi$$49$$\frac{\cos^{\small{-1}}(.6)}{360}\,\approx\,11.78130463\text{ sq. cm.}$
 May 25th, 2012, 09:52 PM #3 Member   Joined: Jul 2009 Posts: 34 Thanks: 0 Re: Area enclosed by a semi-circle and a quarter circle Got it. Thanks. How do you get cos-1(0.6) and cos-1(-06)?
May 25th, 2012, 10:08 PM   #4
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Re: Area enclosed by a semi-circle and a quarter circle

Angle AGD has a cosine of 3/5 and angle GED has a cosine of -3/5. I found these values with the cosine rule.

1. Calculate the area of the kite ADEG and from that subtract the area of circular sector ADG.

2. Calculate the area of circular sector EDG and from that subtract the result of step 1 and that gives you the shaded area.
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 circles.ggb.png (88.8 KB, 321 views)

 May 3rd, 2014, 01:06 AM #5 Newbie   Joined: May 2014 From: Dagupan Posts: 1 Thanks: 0 whoa thanks. got the same problem too.

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