GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
What is the area of ABCDE?
[#permalink]
06 Feb 2020, 10:42
06 Feb 2020, 10:42
1
Expert Reply
1
Bookmarks
00:00
Question Stats:
88% (01:44) correct
11% (02:11) wrong based on 36 sessions
Hide Show timer Statistics
Attachment:
#greprepclub What is the area of ABCDE.PNG [ 2.09 KiB | Viewed 3330 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
Posts: 6218
Given Kudos: 136
Re: What is the area of ABCDE?
[#permalink]
06 Feb 2020, 10:47
06 Feb 2020, 10:47
1
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?
[#permalink]
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)
