3 Color Square
The square is divided into 3 colors: red, yellow, & blue, as shown. The 4 congruent yellow squares are enclosed by the big red cross and 4 congruent blue L-shapes. On the other hand, the 4 congruent yellow rectangles on the edge have the same width as the yellow square but the length twice as long.
Which color has the most area?
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1 solution
From the picture above, when we divide the big square into 6 × 6 smaller squares, each unit square has an equal area to the yellow square because its side length is a half of the blue and a quarter to the red.
By counting these unit blocks, we can see that the red cross-shaped area has 12 unit squares. Each corner blue area has 3 squares, so the total blue area also equals to 12 unit squares. Finally, the 4 edge yellow areas equal to 8 unit squares, so when combined with the overlapping 4 squares, the total yellow area also equals to 12 unit squares.
Hence, all 3 colors have the same area.