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, 2012

Geometry Difficulty 2.5 Junior Find the answer Canada

The diagram shows a square quilt that is made up of identical squares and two sizes of right-angled isosceles triangles. What percentage of the quilt is shaded?

Pick one

Solution

The quilt consists of 25 identical squares.

Of the 25 squares, 4 are entirely shaded, 8 are shaded with a single triangle that covers half of the square, and 4 are shaded with two triangles that each cover a quarter of the square.

Therefore, the shading is equivalent to the area of $4 + 8 \times \frac{1}{2} + 4 \times 2 \times \frac{1}{4} = 10$ squares.

As a percentage, the shading is $\frac{10}{25}\times 100\% = 40\%$ of the total area of the quilt.

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