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 yeoky May 23rd, 2012 09:16 PM

Area enclosed by a semi-circle and a quarter circle

1 Attachment(s)
Find the shaded area, which is enclosed by a square, semi-circle and a quarter of circle.

 greg1313 May 25th, 2012 08:57 PM

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.}$

 yeoky May 25th, 2012 09:52 PM

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)?

 greg1313 May 25th, 2012 10:08 PM

Re: Area enclosed by a semi-circle and a quarter circle

1 Attachment(s)
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.

 nelzekiel May 3rd, 2014 01:06 AM

whoa thanks. got the same problem too. :p

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