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Area of triangular region - GMAT Prep Exam Pack 1

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue May 24, 2016 7:19 am
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In the figure shown, what is the area of triangular region PRT?

1) The area of rectangular region PQST is 24
2) The length of line segment RT is 5
Target question: What is the area of triangular region PRT?

Statement 1: The area of rectangular region PQST is 24
The area of ∆PRT = (base)(height)/2
Statement 1 tells us that (base)(height) = 24
Since the base and the height of the rectangle are the SAME as the base and the height of the triangle PRT, we can use this information to find the area of ∆PRT.
The area of ∆PRT = (base)(height)/2 = 24/2 = 12
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The length of line segment RT is 5
The area of ∆PRT = (base)(height)/2
Statement 2 tells us NOTHING about the base and height, so we can't use this to find the area of ∆PRT.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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Brent
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by [email protected] » Tue May 24, 2016 9:23 am
Hi prata,

Brent's explanation is great, so I won't rehash any of that here.

I do want to point out a minor Geometry rule that you might find useful in certain situations. Notice in this question that the base of the triangle that is inscribed in the rectangle shares a full side with that rectangle? In this situation, the triangle will always have an area that is EXACTLY HALF of the rectangle/square.

You probably won't use this rule too often, but in this question, once it's clear that we're dealing with a triangle inscribed in a rectangle AND we know the rectangle has an area of 24, then we can just take half of 24 to find the area of the triangle.

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by OptimusPrep » Tue May 24, 2016 6:57 pm
prata wrote:Image

In the figure shown, what is the area of triangular region PRT?

1. The area of rectangular region PQST is 24

2. The length of line segment RT is 5
Area of PRT = ?

Statement 1: Area of PQST = 24
NOTE: The area of a triangle = 1/2 area of a rectangle if the base is same.
Reason:
Area of triangle = 1/2*b*h
Area of rectangle = b*h

Hence statement 1 is SUFFICIENT

Statement 2: RT = 5
This does not tell us anything about the area.
INSUFFICIENT

Correct Option: A
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