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MathNet 2012 Question 33

Math Olympiad Vault · MathNet 2012

Question 33

Figure I shows a square of area $40\,\mathrm{cm}^2$, cut into five isosceles right triangles, a square, and a parallelogram, forming the seven pieces of the Tangran game. These pieces can form Figure II, which has a shaded hole. What is the area of the hole?

Question illustration

Figure I

Question illustration

Figure II

A) $5\,\mathrm{cm}^2$; B) $10\,\mathrm{cm}^2$; C) $15\,\mathrm{cm}^2$; D) $20\,\mathrm{cm}^2$; E) $25\,\mathrm{cm}^2$.