It is currently 21 Jan 2018, 06:58

### 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 rectangular coordinate system above, the area of

Author Message
TAGS:

### Hide Tags

Intern
Joined: 05 Jul 2014
Posts: 7

Kudos [?]: 1 [0], given: 38

In the rectangular coordinate system above, the area of [#permalink]

### Show Tags

03 Mar 2016, 15:04
I have solved it slightly differently, please correct me if I am wrong.

Since we know the slanted vertical sides are sized 5 each.

Then I assumed that the shape was half of a square and got it using the formula below

$$5*5*\frac{1}{2}$$=12.5

________________________________________
Nearly at the finish line.

Last edited by seesharp on 13 Mar 2016, 02:19, edited 1 time in total.

Kudos [?]: 1 [0], given: 38

Intern
Joined: 06 Mar 2016
Posts: 3

Kudos [?]: [0], given: 1

Re: In the rectangular coordinate system above, the area of [#permalink]

### Show Tags

10 Mar 2016, 15:10
Do not overwhelm yourself with unnecessary and time-consuming fomulas. There are two common types of triangles on the GMAT, besides 30-60-90 and 45-45-90. The 3:4:5 and 5:12:13 and the apply with multiples.

In this case, the base of the triangle on the right would be 3 (7 - 4) and the height 4, therefore the hypotenuse must be 5. So now we have the base for our formula. For the height, focus on the triangle on the left, which base would be 4 and height 3, therefore its height must be 5. Now we can apply the formula Area= 1/2 * 5 * 5 = 12,5.

Option A

Hope it helps!

Kudos [?]: [0], given: 1

Intern
Joined: 06 Mar 2016
Posts: 3

Kudos [?]: [0], given: 1

Re: In the rectangular coordinate system above, the area of [#permalink]

### Show Tags

10 Mar 2016, 15:12
Do not overwhelm yourself with unnecessary and time-consuming fomulas. There are two common types of triangles on the GMAT, besides 30-60-90 and 45-45-90. The 3:4:5 and 5:12:13 and the apply with multiples.

In this case, the base of the triangle on the right would be 3 (7 - 4) and the height 4, therefore the hypotenuse must be 5. So now we have the base for our formula. For the height, focus on the triangle on the left, which base would be 4 and height 3, therefore its hypotenuse must be 5. Now we can apply the formula. Area= 1/2 * 5 * 5 = 12,5.

Option A

Hope it helps!

Kudos [?]: [0], given: 1

Senior Manager
Joined: 06 Jan 2015
Posts: 281

Kudos [?]: 132 [1], given: 484

Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
In the rectangular coordinate system above, the area of [#permalink]

### Show Tags

31 Aug 2016, 01:47
1
KUDOS
nss123 wrote:
Attachment:
IMAGE PT1.jpg
In the rectangular coordinate system above, the area of triangular region PQR is

(A) 12.5
(B) 14
(C) 10√2
(D) 16
(E) 25

Area Of Triangle =1/2
|0 4 7|
|3 0 4|
|1 1 1|
=1/2(-4(-4) + 7(3))
=12.5

Bunuel Is this method Correct?
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Kudos [?]: 132 [1], given: 484

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1821

Kudos [?]: 1050 [0], given: 5

In the rectangular coordinate system above, the area of [#permalink]

### Show Tags

31 Aug 2016, 15:12
In the rectangular coordinate system above, the area of triangular region PQR is

(A) 12.5
(B) 14
(C) 10√2
(D) 16
(E) 25

We begin by drawing a rectangle that circumscribes the given triangle, creating 3 right triangles, which we label as A, B, and C. Notice that each of these 3 triangles is a right triangle. To determine the area of triangular region PQR, we can subtract the combined areas of triangles A, B, and C from the area of the rectangle.

Let’s determine the area of each right triangle.

Triangle A:

Area = base x height x 1/2

A = 7 x 1 x ½ = 3.5

Triangle B:

A = 4 x 3 x ½ = 6

Triangle C:

A = 3 x 4 x ½ = 6

The sum of the areas of triangles A, B, and C is 3.5 + 6 + 6 = 15.5

Finally we need the area of the rectangle:

Area = length x width

Area = 7 x 4 = 28.

So the area of triangle PQR is 28 – 15.5 = 12.5.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1050 [0], given: 5

Senior Manager
Joined: 22 Nov 2016
Posts: 251

Kudos [?]: 71 [0], given: 42

Location: United States
GPA: 3.4
Re: In the rectangular coordinate system above, the area of [#permalink]

### Show Tags

04 Jul 2017, 11:18
If a triangle is inscribed in a rectangle, its area will be exactly half of the area of the rectangle.

Now lets assume the point Q = (0,4) instead of (0,3) In this case the area of triangle PQR = $$\frac{Area of the imaginary rectangle}{2} = 14$$

According to me the maximum area of this triangle is 14 but it is not 14 because Q = (0,3). The only answer less than 14 is A
_________________

Kudosity killed the cat but your kudos can save it.

Kudos [?]: 71 [0], given: 42

Intern
Joined: 16 Nov 2017
Posts: 4

Kudos [?]: 1 [0], given: 2

In the rectangular coordinate system above, the area of [#permalink]

### Show Tags

15 Dec 2017, 07:36
MrMicrostrip wrote:
by calculating area of different different region is a good approach but not effective when you just have 2 sec. left.
I have generated one effective way to solve these type of problem.
here we know that Q has coordinates (0,3) so measure it roughly through your pencil or pen, now we have one task left that is to measure height of a triangle.
So from the measured distance we can predict the height of a triangle which comes to be 3.60 approx. in this question thus Area will be 12.6(approx.) hence option A is 99.99% correct.
Hopefully you will enjoy to use this approach!

It is a good approach, the way I solved it was:

the base is 7 (fact). the height is no more than 4 and no less than 3 (fact) so the area:

$$21*0.5 < A < 28*0.5$$

So answer MUST be between 10.5 and 14. only one answer fits

Kudos [?]: 1 [0], given: 2

In the rectangular coordinate system above, the area of   [#permalink] 15 Dec 2017, 07:36

Go to page   Previous    1   2   [ 27 posts ]

Display posts from previous: Sort by