Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 2.1 Junior Find the answer

What is the side length of the larger square if a small square is drawn inside a larger square, and the area of the shaded region and the area of the unshaded region are each $18 \mathrm{~cm}^{2}$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since the area of the larger square equals the sum of the areas of the shaded and unshaded regions inside, then the area of the larger square equals $2 \times 18 \mathrm{~cm}^{2}=36 \mathrm{~cm}^{2}$ .
Since the larger square has an area of $36 \mathrm{~cm}^{2}$ , then its side length is $\sqrt{36 \mathrm{~cm}^{2}}=6 \mathrm{~cm}$ .

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