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 the shaded region in the figure above, i
[#permalink]
13 Sep 2020, 08:30
13 Sep 2020, 08:30
Expert Reply
2
Bookmarks
00:00
Question Stats:
60% (03:26) correct
39% (02:30) wrong based on 28 sessions
Hide Show timer Statistics
Attachment:
GRE What is the area of the shaded region.png [ 12.61 KiB | Viewed 4503 times ]
What is the area of the shaded region in the figure above, in terms of a, b, and c ?
A. \(\sqrt{3} (a^2+b^2+c^2)\)
B. \(\frac{\sqrt{3}}{2}\) \((a^2-b^2-c^2)\)
C. \(\frac{\sqrt{3}}{2}\) \((a^2-b^2+c^2)\)
D. \(\frac{\sqrt{3}}{2}\) \((a^2+b^2-c^2)\)
E. \(\frac{\sqrt{3}}{2}\) \((a^2+b^2+c^2)\)
Re: What is the area of the shaded region in the figure above, i
[#permalink]
14 Sep 2020, 21:48
14 Sep 2020, 21:48
3
by using pythagoras theorem for triangle ABC
\((2a)^2=x^2+((a√3)^2)\) (let x be unknown side of triangle ABC)
then x=a
area of big triangle =(1/2)*a*a√3=\((√3/2)*a^2\)
we need to remove the area of unshaded region to get area of shaded region
lets find area of unshaded region
from ΔDGH ∠D=30 and HG=b-c
then DG=√3(b-c) (by applying tan formula)
area of ΔDGH=\((√3(b-c)^2 /2)\)------(2)
now area of ▭DEFG = √3(b-c)*c
we can write this as=\((√3/2)*(2bc-2c^2)\) -----(3)
total area of unshaded region=\((√3/2)*(b^2-c^2)\)
now total area of shaded region will be eqn(1)-eqn(3)=\((√3/2)*(a^2-b^2+c^2)\)
option C is correct
\((2a)^2=x^2+((a√3)^2)\) (let x be unknown side of triangle ABC)
then x=a
area of big triangle =(1/2)*a*a√3=\((√3/2)*a^2\)
we need to remove the area of unshaded region to get area of shaded region
lets find area of unshaded region
from ΔDGH ∠D=30 and HG=b-c
then DG=√3(b-c) (by applying tan formula)
area of ΔDGH=\((√3(b-c)^2 /2)\)------(2)
now area of ▭DEFG = √3(b-c)*c
we can write this as=\((√3/2)*(2bc-2c^2)\) -----(3)
total area of unshaded region=\((√3/2)*(b^2-c^2)\)
now total area of shaded region will be eqn(1)-eqn(3)=\((√3/2)*(a^2-b^2+c^2)\)
option C is correct
Attachments
pc2.jpg [ 9.67 KiB | Viewed 4403 times ]
Re: What is the area of the shaded region in the figure above, i
[#permalink]
24 Jan 2021, 08:50
24 Jan 2021, 08:50
