Nice Area Problem (1)

Geometry Level 3

Each of the four pink triangles has one of their vertices at a corner of the blue 5 × 5 5\times 5 square.

What percentage of the square is pink?


The answer is 30.

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1 solution

Hana Wehbi
May 10, 2018

The area of triangle A = 3 × 1 2 = 1.5 A =\frac{3\times1}{2}=1.5 .

The area of triangle B = 2 × 2 2 = 2.0 B= \frac{2\times 2}{2}=2.0 .

The area of triangle C = 3 × 2 2 = 3.0 C=\frac{3\times2}{2}=3.0 .

The area of triangle D = 2 × 1 2 = 1.0 D=\frac{2\times1}{2}=1.0 .

Adding all these Areas of triangles A, B, C and D is 7.5 7.5 , where the area of the big blue square is 5 × 5 = 25 5\times5=25 .

Thus, the ratio of the area of the triangles to the area of the square is 7.5 25 = 30 100 = 30 % \frac{7.5}{25}=\frac{30}{100}= 30\% .

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