# Paper square diagonal

A paper square has diagonal length 6 in. two folders are made along lines perpendicular to the diagonal and through trisection points A and B. By what percentage has the visible area of the paper decreased?

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Do you know the Pythagorean Theorem? – process91 Dec 16 '12 at 18:17

Hints:

• Draw a picture

• What proportion of the original square is represented by the white triangles?

• If you stick the white triangles together you get a square whose sides are two-thirds of the sides of the original square. So what is the ratio of the areas? What is that as a percentage?

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HINT: Look at the figure below; the area that you’re losing is the area of the red triangle plus the area of the mirror-image triangle at A. Since $|AB|=6$, $|CB|=2$, and the red triangle is an isosceles right triangle, so all of its dimensions are easily calculated from that. Once you have the area of the triangles, calculate the area of the whole square $-$ you know its diagonal, so you can find its side length using the Pythagorean theorem $-$ and see what percentage the triangles’ area is of the whole thing.

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