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In the rectangular coordinate system above, the area of

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

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New post 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








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

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

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New post 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!

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New post 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!

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

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New post 31 Aug 2016, 01:47
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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?
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In the rectangular coordinate system above, the area of [#permalink]

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New post 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.

Image

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.

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

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

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New post 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

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

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