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What is the area of ABCDE?
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06 Feb 2020, 10:42
06 Feb 2020, 10:42
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89% (01:44) correct
10% (02:11) wrong based on 38 sessions
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#greprepclub What is the area of ABCDE.PNG [ 2.09 KiB | Viewed 3433 times ]
What is the area of ABCDE?
A. 108
B. 126
C. \(144 - 6\sqrt{3}\)
D. \(144 - 18\sqrt{3}\)
E. \(144 - 36\sqrt{3}\)
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
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Re: What is the area of ABCDE?
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06 Feb 2020, 10:47
06 Feb 2020, 10:47
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Carcass wrote:
Attachment:
#greprepclub What is the area of ABCDE.PNG
What is the area of ABCDE?
A. 108
B. 126
C. \(144 - 6\sqrt{3}\)
D. \(144 - 18\sqrt{3}\)
E. \(144 - 36\sqrt{3}\)
Kudos for the right answer and explanation
Let's add a line from A to D:
When we do this, we see that ABCD is a square, and ADE is an equilateral triangle.
We can also write: area of ABCDE = (area of square ABCD) - (area of equilateral triangle ADE)
Useful formula: Area of equilateral triangle = (√3)(side²)/4
We get: ABCDE = (12²) - ((√3)(12²)/4)
Simplify: ABCDE = 144 - 36√3
Answer: E
Cheers,
Brent
Re: What is the area of ABCDE?
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06 Feb 2020, 10:53
06 Feb 2020, 10:53
1
Total Square area is =a*a=12*12=144
Then area of triangle ADE = ?
here we can angle EAD(angle a) and EDA(angle d) are both 60(90- 30) since it has form a square.then ultimately the remaining angle also 60 (180-120)..so equilateral triangle
so,area of ADE= root(3)/4(a*a)=root(3)/4(12*12)=36 root(3);
so answer is 144-36root(3)
Then area of triangle ADE = ?
here we can angle EAD(angle a) and EDA(angle d) are both 60(90- 30) since it has form a square.then ultimately the remaining angle also 60 (180-120)..so equilateral triangle
so,area of ADE= root(3)/4(a*a)=root(3)/4(12*12)=36 root(3);
so answer is 144-36root(3)
