It is currently 17 Nov 2017, 10:36

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the figure above, all triangles have the same area. If the area of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42250

Kudos [?]: 132495 [0], given: 12323

In the figure above, all triangles have the same area. If the area of [#permalink]

### Show Tags

11 Nov 2017, 06:57
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:17) correct 0% (00:00) wrong based on 11 sessions

### HideShow timer Statistics

In the figure above, all triangles have the same area. If the area of the shaded region is 84, and the area of square PQRS is 100, what is the total area of the regions outlined by the heavy line?

(A) 16
(B) 92
(C) 108
(D) 116
(E) 132

[Reveal] Spoiler:
Attachment:

2017-11-11_1745_002.png [ 53.1 KiB | Viewed 204 times ]

The OA will be automatically revealed on Saturday 18th of November 2017 05:57:25 AM Pacific Time Zone
_________________

Kudos [?]: 132495 [0], given: 12323

Director
Joined: 22 May 2016
Posts: 968

Kudos [?]: 335 [0], given: 587

In the figure above, all triangles have the same area. If the area of [#permalink]

### Show Tags

11 Nov 2017, 07:55
Bunuel wrote:

In the figure above, all triangles have the same area. If the area of the shaded region is 84, and the area of square PQRS is 100, what is the total area of the regions outlined by the heavy line?

(A) 16
(B) 92
(C) 108
(D) 116
(E) 132

[Reveal] Spoiler:
Attachment:
2017-11-11_1745_002.png

The area of the shaded region is the area of the square minus 4 of the 8 triangles with the same area. So

The (area of the shaded region) equals the (area of the square) minus ($$\frac{1}{2}$$ the area of all the congruent triangles), $$\frac{1}{2}T$$:
$$84 = 100 - \frac{1}{2}T$$
$$\frac{1}{2}T = (100 - 84) = 16$$

The area enclosed by the thick outline equals the square plus $$\frac{1}{2}$$ the area of the all the triangles:
Area = $$100 + \frac{1}{2}T$$
$$\frac{1}{2}T = 16$$

Area enclosed by thick outline = $$100 + 16 = 116$$

Kudos [?]: 335 [0], given: 587

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3097

Kudos [?]: 1114 [0], given: 327

Location: India
GPA: 3.5
Re: In the figure above, all triangles have the same area. If the area of [#permalink]

### Show Tags

11 Nov 2017, 08:02
Bunuel wrote:

In the figure above, all triangles have the same area. If the area of the shaded region is 84, and the area of square PQRS is 100, what is the total area of the regions outlined by the heavy line?

(A) 16
(B) 92
(C) 108
(D) 116
(E) 132

[Reveal] Spoiler:
Attachment:
2017-11-11_1745_002.png

Area of shaded region + Area of 4 Triangles = Area of the square

So, 84 + Area of 4 Triangles = 100

So, Area of 4 Triangles = 100 - 84

Or, Area of 4 Triangles = 16

Since, Area of each triangle = 4

Since all the triangles are of equal area , the area of the total figure = Area of the square + area of 4 trinagles

Or, Area of the total figure = 100 + 16

Or, Area of the total figure = 116, answer will be (D)

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1114 [0], given: 327

Re: In the figure above, all triangles have the same area. If the area of   [#permalink] 11 Nov 2017, 08:02
Display posts from previous: Sort by