2002 AMC 12A Problem 8

Problem 8 of 25EasierGeometry

Betsy designed a flag using blue triangles, small white squares, and a red center square, as shown. Let

B

be the total area of the blue triangles,

W

the total area of the white squares, and

R

the area of the red square. Which of the following is correct?

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Solution

Drawing the diagonals shown, the entire flag is tiled by congruent triangles. Counting, there are

24

triangles in the blue region,

24

in the white region, and

16

in the red square. Since the blue and white regions contain the same number of triangles,

B = W.

Thus, the correct answer is A.