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In the figure above, rectangle ABCD is attached to semicircle CFD. If

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In the figure above, rectangle ABCD is attached to semicircle CFD. If  [#permalink]

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New post 18 Nov 2015, 23:58
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In the figure above, rectangle ABCD is attached to semicircle CFD. If CE = ED, \(AC = 6\sqrt{2}\) and EF = 3, what is the area of the figure ABCFD?

A. \(36 + \frac{9\pi}{2}\)

B. \(36 + \frac{3\pi}{2}\)

C. \(36 + 3\pi\)

D. \(12+ \frac{3\pi}{2}\)

E. \(12+ \frac{9\pi}{2}\)


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Re: In the figure above, rectangle ABCD is attached to semicircle CFD. If  [#permalink]

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New post 19 Nov 2015, 00:19
CD = 6
AC = 6root2
Therefore AD = 6
Area of ABCD = 6 * 6= 36
Area of semi circle = πr^2/2 = π*9/2
Total area of ABCFD = 36 + π*9/2
Answer : A
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In the figure above, rectangle ABCD is attached to semicircle CFD. If  [#permalink]

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New post 28 Jul 2018, 09:08
Bunuel wrote:
Image
In the figure above, rectangle ABCD is attached to semicircle CFD. If CE = ED, \(AC = 6\sqrt{2}\) and EF = 3, what is the area of the figure ABCFD?

A. \(36 + \frac{9\pi}{2}\)

B. \(36 + \frac{3\pi}{2}\)

C. \(36 + 3\pi\)

D. \(12+ \frac{3\pi}{2}\)

E. \(12+ \frac{9\pi}{2}\)


Attachment:
Untitled.png


So would it be fair to say that ABCD is actually a square since AD=CD?
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Re: In the figure above, rectangle ABCD is attached to semicircle CFD. If  [#permalink]

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New post 28 Jul 2018, 09:19
MikeScarn wrote:
Bunuel wrote:
Image
In the figure above, rectangle ABCD is attached to semicircle CFD. If CE = ED, \(AC = 6\sqrt{2}\) and EF = 3, what is the area of the figure ABCFD?

A. \(36 + \frac{9\pi}{2}\)

B. \(36 + \frac{3\pi}{2}\)

C. \(36 + 3\pi\)

D. \(12+ \frac{3\pi}{2}\)

E. \(12+ \frac{9\pi}{2}\)


Attachment:
Untitled.png


So would it be fair to say that ABCD is actually a square since AD=CD?


Yes, you are correct..
Since CD is twice the radius =2*3=6 and hypotenuse=6√2
So third side =√{(6√2)^2-6^2}=√{72-36}=√36=6
As you have said sides are equal
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Re: In the figure above, rectangle ABCD is attached to semicircle CFD. If  [#permalink]

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New post 28 Jul 2018, 09:37
chetan2u Cool, thanks buddy.
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Re: In the figure above, rectangle ABCD is attached to semicircle CFD. If &nbs [#permalink] 28 Jul 2018, 09:37
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