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Vanishing area


(I don't understand how to load up images here, so see attached)

Ignore my poor attempts at Microsoft Paint for a second and presume that the same colors produce congruent pieces.


When a student of mine calculated the individual combined pieces they found the area to be 59 sq. units but when they put them together and use the area formula they, they found the area to be 60 sq units and again, when they changed the orientation of the pieces to make another version and used the area formula they found the area to be 58 sq. units. What's going on here?


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1 answer to this question

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The diagonal lines in both resulting "triangles" are not straight making them pentagons rather than triangles. They have a slight kink since 2x5 and 3x7 triangles don't have the same angles. The difference is not noticable, but the "triangle" on the left has concave sides, while the "triangle" on the right has convex sides making up for the difference in the area.

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