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What is the area of ABCDE?

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What is the area of ABCDE?  [#permalink]

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New post 25 Mar 2015, 01:38
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

91% (01:24) correct 9% (03:52) wrong based on 33 sessions

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Attachment:
sawtooth_figure (2).PNG
sawtooth_figure (2).PNG [ 4.1 KiB | Viewed 1277 times ]


What is the area of ABCDE?

A. \(144 + 36\sqrt{3}\)
B. \(144 + 18\sqrt{3}\)
C. \(144 + 12\sqrt{3}\)
D. 162
E. 153

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Re: What is the area of ABCDE?  [#permalink]

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New post 25 Mar 2015, 08:18
PareshGmat wrote:
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What is the area of ABCDE?

A. \(144 + 36\sqrt{3}\)
B. \(144 + 18\sqrt{3}\)
C. \(144 + 12\sqrt{3}\)
D. 162
E. 153



hi,
again Q can be simplified by joining A and D..
the area of ABCDE= area of square ABCD + area of eq triangle= \(144 + 36\sqrt{3}\)
ans A
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Re: What is the area of ABCDE?  [#permalink]

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New post 07 Oct 2018, 00:05
Joining A and D, AD =12 and the figure is a square with all angles = 90 deg. and all sides being equal.
Area of ABCD = 12x12 = 144 sq. units
Area of ADE is an equilateral triangle. Area = sqrt.3/4*12^2 = 36sqrt.3

Total area = 144 + 36 sqrt.3 (A)
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Re: What is the area of ABCDE?  [#permalink]

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New post 07 Oct 2018, 01:49
OA: A

Joining A and D, we get an equilateral triangle and square with side \(a = 12\)

total area \(= a^2+ \frac{\sqrt{3}}{4}a^2 = 12^2+\frac{\sqrt{3}}{4}*12^2 =144+36\sqrt{3}\)
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Re: What is the area of ABCDE?  [#permalink]

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New post 07 Oct 2018, 02:16
PareshGmat wrote:
Attachment:
sawtooth_figure (2).PNG


What is the area of ABCDE?

A. \(144 + 36\sqrt{3}\)
B. \(144 + 18\sqrt{3}\)
C. \(144 + 12\sqrt{3}\)
D. 162
E. 153



JOIN AD, so AD is || to BC and hence ABCD is a square...so Area = 12*12= 144

Now since ABCD is square angle BAD = angle ADC =angle ABC = angle BCD = 90 (all angles of square is 90 degrees)

so angle AED = 150 - angle BAD = 60
angle EDA = 150- angle ADC = 60
so AED is also 60 as sum of all angles in a triangle is 180
so AED is an equilateral triangle with side = 12

so total area of equilateral triangle ED = sqrt (3)/4 *12*12 = 36 sqrt 3

so total area of figure= area of square. ABCD + area of equilateral triangle AED = 144+ 36 sqrt 3

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Re: What is the area of ABCDE? &nbs [#permalink] 07 Oct 2018, 02:16
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