Trapezoidian variablilian

Geometry Level 2

Find the area of the shaded region in the figure.

x 2 + x y 4 \frac {x^2 +xy}{4} x 2 + y 2 2 \frac {x^2 +y^2}{2} x 2 − y 2 2 \frac {x^2 -y^2}{2} x 2 + y 2 x^2 + y^2

Yellow Tomato by Yellow Tomato , 17, USA

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1 solution

Harish Sasikumar
Oct 22, 2015

This is an easy way to figure out the answer from the list of choices & is not a complete solution.

Consider two extreme cases.

When y=0, answer has to be x 2 / 2 x^{2}/2 .

When y=x, answer has to be 0.

The only choice satisfying both these conditions is ( x 2 − y 2 ) / 2 (x^{2}-y^{2})/2

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