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What is the area of triangle??

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by sbhawal » Fri Nov 29, 2013 9:19 am
Another question that I came across in GMAT Prep

Question : What is the area of the triangle PQR given P(4,0) Q(0,3) R(7,4)?
A. 12.5
B. 14
C. 10√2
D. 16
E. 25

Answer: [spoiler]A[/spoiler]
Though this sounds simple, I aint able to solve it... :oops:
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by Mathsbuddy » Fri Nov 29, 2013 9:48 am
You could:
1)Draw a sketch of PQR on x-y axes.
2)Now draw a rectangle to surround it, vertices: (0,0), (0,4), (7,0), (7,4)
3) Work out the area of the rectangle R = 7 * 4 = 28
4) Work out the areas of the 3 triangles inside the rectangle that surround triangle PQR:
Triangle 1: Area = 1 * 7/2 = 3.5
Triangle 2: Area = 4 * 3/2 = 6
Triangle 3: Area = 3 * 4/2 = 6
Sum of 3 triangle areas, S = 15.5
5) Subtract R - S = 28 - 15.5 = 12.5

Answer (A) 12.5

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by theCodeToGMAT » Fri Nov 29, 2013 9:50 am
So, its a right angled triangle==> 1/2 * 5 * 5 = 12.5
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by sbhawal » Fri Nov 29, 2013 10:10 am
Thanks mathsbuddy!!
Now I get it!!
Mathsbuddy wrote:You could:
1)Draw a sketch of PQR on x-y axes.
2)Now draw a rectangle to surround it, vertices: (0,0), (0,4), (7,0), (7,4)
3) Work out the area of the rectangle R = 7 * 4 = 28
4) Work out the areas of the 3 triangles inside the rectangle that surround triangle PQR:
Triangle 1: Area = 1 * 7/2 = 3.5
Triangle 2: Area = 4 * 3/2 = 6
Triangle 3: Area = 3 * 4/2 = 6
Sum of 3 triangle areas, S = 15.5
5) Subtract R - S = 28 - 15.5 = 12.5

Answer (A) 12.5

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by Brent@GMATPrepNow » Fri Nov 29, 2013 12:18 pm
Here's a similar question to practice with:
- https://www.beatthegmat.com/geometry-que ... 70467.html

Cheers,
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by GMATGuruNY » Fri Nov 29, 2013 4:37 pm
Question : What is the area of the triangle PQR given P(4,0) Q(0,3) R(7,4)?
A. 12.5
B. 14
C. 10√2
D. 16
E. 25
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The area of the rectangle drawn around triangle PQR = 7*4 = 28.
Since triangle PQR takes up less than half the rectangle, PQR < 14.

The correct answer is A.
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by [email protected] » Fri Nov 29, 2013 6:12 pm
Hi sbhawal,

The other responses to this post each provide explanation and insight into this question. Here are some tactics to keep in mind as you come across these issues in future questions:

1) Many graphing questions can be made easier to solve by graphing them.
2) Any diagonal line on a graph is part of a right triangle. You can draw that triangle to figure out the length of the line and the area of the triangle.

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