Last visit was: 13 Sep 2026, 18:55 It is currently 13 Sep 2026, 18:55
Home
Messages
Tests
Schools
Events
Close
GMAT 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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
605-655 (Medium)|   Geometry|      
User avatar
Sajjad1994
User avatar
GRE Forum Moderator
Joined: 02 Nov 2016
Last visit: 13 Sep 2026
Posts: 16,401
Own Kudos:
53,717
 [3]
Given Kudos: 6,462
GPA: 3.62
Products:
Forum Quiz
Posts: 16,401
Kudos: 53,717
 [3]
In the figure to the right, both triangles are right triangles. The ar 26 May 2017, 11:18
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

67% (01:59) correct 33% (01:38) wrong based on 85 sessions

History

Date
Time
Result
Not Attempted Yet
In the figure BELOW, both triangles are right triangles. The area of the shaded region is

(A) 1/2
(B) 2/3
(C) 7/8
(D) 3/2
(E) 5/2

Nova GMAT
ShowHide Answer
Official Answer
C

Attachments

MMMMKKK.jpg
MMMMKKK.jpg [ 6.22 KiB | Viewed 6919 times ]

User avatar
mikemcgarry
User avatar
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Last visit: 06 Aug 2018
Posts: 4,475
Own Kudos:
31,136
 [3]
Given Kudos: 130
Expert
Expert reply
Posts: 4,475
Kudos: 31,136
 [3]
In the figure to the right, both triangles are right triangles. The ar 26 May 2017, 13:11
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SajjadAhmad
In the figure BELOW, both triangles are right triangles. The area of the shaded region is

(A) 1/2
(B) 2/3
(C) 7/8
(D) 3/2
(E) 5/2

Nova GMAT
Show more
Dear SajjadAhmad,

I'm happy to respond. :-)

This is quite straightforward.
Attachment:
similar right triangles.png
similar right triangles.png [ 13.23 KiB | Viewed 6943 times ]
We know we have (angle ACB) = (angle AED) = 90 degrees.
We have AE = DE = 2, so the area of triangle ADE is 2.

The two triangles must be similar, because they share right angles and the angle at A. Because AE = DE, we know that AC = BC = 3/2.

The area of triangle ABC = (1/2)bh = (1/2)(3/2)(3/2) = 9/8

shaded region = (area of triangle ADE) - (area of triangle ABC) = 2 - 9/8 = 7/8

Answer = (C)

Does all this make sense?
Mike :-)
User avatar
Sajjad1994
User avatar
GRE Forum Moderator
Joined: 02 Nov 2016
Last visit: 13 Sep 2026
Posts: 16,401
Own Kudos:
53,717
 [1]
Given Kudos: 6,462
GPA: 3.62
Products:
Forum Quiz
Posts: 16,401
Kudos: 53,717
 [1]
In the figure to the right, both triangles are right triangles. The ar 26 May 2017, 22:55
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mikemcgarry
SajjadAhmad
In the figure BELOW, both triangles are right triangles. The area of the shaded region is

(A) 1/2
(B) 2/3
(C) 7/8
(D) 3/2
(E) 5/2

Nova GMAT
Dear SajjadAhmad,

I'm happy to respond. :-)

This is quite straightforward.
Attachment:
similar right triangles.png
We know we have (angle ACB) = (angle AED) = 90 degrees.
We have AE = DE = 2, so the area of triangle ADE is 2.

The two triangles must be similar, because they share right angles and the angle at A. Because AE = DE, we know that AC = BC = 3/2.

The area of triangle ABC = (1/2)bh = (1/2)(3/2)(3/2) = 9/8

shaded region = (area of triangle ADE) - (area of triangle ABC) = 2 - 9/8 = 7/8

Answer = (C)

Does all this make sense?
Mike :-)
Show more

Hi Mike

Thanks God you didn't say it is a bad quality question or non-GMAT type or Flawed Question :)
Thanks for Solution
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,790
Own Kudos:
6,356
 [1]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,790
Kudos: 6,356
 [1]
In the figure to the right, both triangles are right triangles. The ar 31 May 2017, 13:03
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Another way to do this question is as follows:

The shaded region comprises of both
a rectangle of dimensions 2- 3/2(1/2)(breadth) and 3/2(length) and
a triangle with dimensions 1/2(base) and 1/2(height).

The area for the rectangle is 3/4(3/2*1/2)
Similarly the area of the triangle is
(1/2)*(1/2)*(1/2) = 1/8

Added the sum for area of the shaded portion is 3/4 + 1/8 or 7/8(Option C)

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
User avatar
VyshakhR1995
User avatar
Joined: 02 Mar 2017
Last visit: 28 Jul 2019
Posts: 227
Own Kudos:
782
Given Kudos: 30
Location: India
Concentration: Finance, Marketing
Posts: 227
Kudos: 782
In the figure to the right, both triangles are right triangles. The ar 31 May 2017, 13:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The triangles are similar.
Area of large on is 1/2*2*2
area of small one 1/2 *3/2 * 3/2
Shaded region = 2 - 9/8
7/8 is the answer
User avatar
zaidi1212
User avatar
Joined: 18 Dec 2021
Last visit: 01 Apr 2026
Posts: 28
Own Kudos:
2
Given Kudos: 195
Location: Germany
Concentration: Economics, Entrepreneurship
Schools: Booth '25
GPA: 3.25
Products:
My Reviews
Schools: Booth '25
Posts: 28
Kudos: 2
In the figure to the right, both triangles are right triangles. The ar 08 Dec 2022, 10:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Area of the larger triangle: 2*2*1/2 = 2
Area of the smaller traingle: 1/2 * 3/2 * 3/2 = 9/8

Area of the shaded region = 2 - 3/8 = 16-9/8 = 7/8
Moderator:
Bunuel
Math Expert
113482 posts