Geom etry one day geo met ry

Geometry Level 3

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Arko Roychoudhury by arko roychoudhury , 20, India

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1 solution

Caleb Townsend
Mar 21, 2015

The shaded area is a trapezoid of area A = h ( x + y 2 ) . A = h (\frac{x+y}{2}). The unshaded area is an isosceles right triangle (as it is similar to the large triangle), therefore the unknown leg length is equal to y . y. So h = x − y . h = x - y. Substituting into the area equation above, A = 1 2 ( x − y ) ( x + y ) = x 2 − y 2 2 A = \frac{1}{2}(x-y)(x+y) \\ = \boxed{\frac{x^2 - y^2}{2}}

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