Area of the first square = 16. Side = 4.
Area of the tilted square = 25. Side = 5.
The side of the tilted square becomes the hypotenuse of the triangle = 5.
The side of the first square becomes the height of the triangle. = 4.
Then by Pythagoras theorem, the base is 3.
Area of the triangle = 1/2*4*3 = 6.

A is the answer.

Hi All,

We're told that the two squares have areas 16 and 25, respectively. We're asked for the AREA of the shaded triangular region. This is an example of how the GMAT writers sometimes like to 'hide' the special Right Triangles (re: 3/4/5, 5/12/13, 30/60/90 and 45/45/90) in Geometry questions - and if you recognize the patterns involved, then you can answer this question relatively quickly without too much work.

To start, based on the areas of the two squares, we know that their respective sides are 4s and 5s. Thus, the right triangle has a height of 4 and a hypotenuse of 5. You probably recognize this as a 3/4/5 right triangle, but even if you didn't, you can use the Pythagorean Theorem to prove it:

A^2 + B^2 = C^2
A^2 + 4^2 = 5^2
A^2 + 16 = 25
A^2 = 9
A = 3... since this is a shape, it can't have a "negative" side (so -3 is not an option).

With a height of 4 and a base of 3, we can determine the AREA of the shape:
A = (1/2)(base)(height)
A = (1/2)(3)(4)
A = 6

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Solution:

Since the triangle is a right triangle with hypotenuse = √25 = 5 and a leg √16 = 4, it must be a 3-4-5 right triangle. Therefore, the area of the triangle is ½ x 3 x 4 = 6.

Answer: A
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Side pertaining to altidtude of triangle is 4 & Side pertaining to altidtude of triangle is 5

Thus base of the triangle will be 3 (USing Pythagorean Triples )

So, Area of the shaded triangle is \(\frac{3*4}{2}=6\), Answer must be (A)
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