Note that the question mentions largest and smallest squares which makes us assume that the leftmost quadrilateral should be a square too but it should be explicitly mentioned.

Assume that the figure lies on the co-ordinate axis as shown.

The base of the required triangle lies on a line which is 45 degrees to the y axis (the red line)

The third vertex of the triangle lies on the dotted line which is also 45 degrees to the y axis. Hence these two lines are parallel and vertical distance between them will always be the same (the green lines)

No matter what the actual size of the leftmost square (as shown by three different squares), the altitude of the triangle will be the green line only.

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Base of the triangle is the diagonal of the square of side 1. So the length of the diagonal is \(\sqrt{2}\)

Altitude of the triangle is the diagonal of teh square of side 2. So the length of the diagonal is \(2\sqrt{2}\)

Area of triangle = \((1/2)*\sqrt{2}*2*\sqrt{2} = 2\)

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Karishma

Veritas Prep GMAT Instructor

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