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UKMT Intermediate Mathematical Challenge, 2020

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The diagram shows an isosceles right-angled triangle which has a hypotenuse of length $y$ . The interior of the triangle is split up into identical squares and congruent isosceles right-angled triangles. What is the total shaded area inside the triangle?

(A) $\dfrac{y^2}{2}$ (B) $\dfrac{y^2}{4}$ (C) $\dfrac{y^2}{8}$ (D) $\dfrac{y^2}{16}$ (E) $\dfrac{y^2}{32}$

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