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What is the area of triangle??

This topic has 3 expert replies and 3 member replies

What is the area of triangle??

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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: A
Though this sounds simple, I aint able to solve it... Embarassed

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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

Does this help?

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So, its a right angled triangle==> 1/2 * 5 * 5 = 12.5
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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

Does this help?

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GMAT/MBA Expert

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Here's a similar question to practice with:
- http://www.beatthegmat.com/geometry-ques-from-gmatprep-t270467.html

Cheers,
Brent

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Quote:
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


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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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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