Math CentralQuandaries & Queries


Question from Shirley, a parent:

A square is inscribed within a square that has a side the measures 16 centimeters. The vertices of the smaller square are located at the midpoints of the sides of the larger square. What is the area of the larger square, area of a smaller square, the probability that a point chosen at random is in the
shaded are? Express the answer as a simplified fraction.


The key to solving this problem is Pythagoras theorem. When you join the midpoints of two adjacent sides of the larger square you form a right triangle with legs of length 16/2 = 8 cm. The hypotenuse of this triangle is a side of the smaller square. What is the length of this side?


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