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Equilateral triangle AED lies inside square ABCD, as shown above. If

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Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

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New post 20 Oct 2016, 23:15
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Equilateral triangle AED lies inside square ABCD, as shown above. If the side of the square is 6, what is the area of the shaded region?

A. \(19-9\sqrt{3}\)

B. \(36-18\sqrt{3}\)

C. \(9\sqrt{3}\)

D. \(3(12-3\sqrt{3})\)

E. \(2(9+3\sqrt{3})\)

Attachment:
T7902.png
T7902.png [ 7.59 KiB | Viewed 2481 times ]

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Re: Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

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New post 21 Oct 2016, 12:02
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Bunuel wrote:
Image
Equilateral triangle AED lies inside square ABCD, as shown above. If the side of the square is 6, what is the area of the shaded region?

A. \(19-9\sqrt{3}\)

B. \(36-18\sqrt{3}\)

C. \(9\sqrt{3}\)

D. \(3(12-3\sqrt{3})\)

E. \(2(9+3\sqrt{3})\)

Attachment:
T7902.png


Area of shaded region = Area of Square - Area of the Equilateral Triangle

Area of the square \(= 6^2 = 36\)

Area of the Equilateral Triangle =\(\frac{√3}{4}*6^2\) = \(9√3\)

So, Area of shaded region = \(36\) \(-\) \(9√3\)

Or, Area of shaded region = \(3(12-3\sqrt{3})\)

Answer will be (D)

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Re: Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

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New post 21 Oct 2016, 12:36
Bunuel wrote:
Image
Equilateral triangle AED lies inside square ABCD, as shown above. If the side of the square is 6, what is the area of the shaded region?

A. \(19-9\sqrt{3}\)

B. \(36-18\sqrt{3}\)

C. \(9\sqrt{3}\)

D. \(3(12-3\sqrt{3})\)

E. \(2(9+3\sqrt{3})\)

Attachment:
T7902.png





the side of the equilateral triangle is 6 as theside of the square.

the height of an equilateral triangle is equal to \(\frac{side}{2}*\sqrt{3}\) = \(3\sqrt{3}\)

the area of the triangle is \(\frac{1}{2}*6*3*\sqrt{3}\) = \(9\sqrt{3}\)

the area of the square is \(6*6 = 36\)

the difference between the area of the square and the area of the triangle is \(36-\)\(9\sqrt{3}\) \(= 3*(12+3\sqrt{3})\)

answer D
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Re: Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

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New post 21 Oct 2016, 17:48
Bunuel wrote:
Image
Equilateral triangle AED lies inside square ABCD, as shown above. If the side of the square is 6, what is the area of the shaded region?

A. \(19-9\sqrt{3}\)

B. \(36-18\sqrt{3}\)

C. \(9\sqrt{3}\)

D. \(3(12-3\sqrt{3})\)

E. \(2(9+3\sqrt{3})\)

Attachment:
T7902.png


Area of the square = 6*6 = 36
Since the triangle is an equilateral triangle and shares one side with the square, side of the triangle = 6

Area of the triangle = (√3/4)*6^2 = 9√3

Area of the shaded region = 36 - 9√3 = 3(12 - 3√3)

Correct Option: D
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Re: Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

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New post 22 Oct 2016, 03:55
This seems to be formula based

Area of square = a ^2 = 36

Area of equilateral triangle = Sq rt 3/4 * a^2
= 9 * sq rt 3

Area of shaded region = 36 - 9*sq rt 3
= 3(12−3√3)

Option D

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Re: Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

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Re: Equilateral triangle AED lies inside square ABCD, as shown above. If &nbs [#permalink] 08 Jul 2018, 22:12
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