Answer: 72 square cm
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Explanation
The blue plus sign can be thought of as overlapping a long 20 by 2 rectangle over top a tall skinny 4 by 10 rectangle (or vice versa).
- 20 by 2 rectangle has area 20*2 = 40 square cm
- 4 by 10 rectangle has area 4*10 = 40 square cm
That's 40+40 = 80 square cm. But wait, we have the overlapped 2 by 4 rectangular region in the very center. That region's area is counted twice when we added those 40s.
So we need to subtract off 2*4 = 8 to get 80-8 = 72 square cm
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Here are some other approaches you could do:
- Break the blue plus sign into a tall skinny rectangle in the middle, with two smaller blue rectangles on either side.
- Break the blue plus sign into long stretched out flat rectangle in the middle, with two smaller blue rectangles on top and bottom.
- Break the plus sign into 5 smaller rectangles. There's one small rectangle in the middle surrounded by 4 rectangles in the north, east, south, and west directions.
- Find the area of the entire rectangle (20*10 = 200) and then subtract off the areas of each white rectangle to get the area of the blue region. Hint: Each white rectangle has the same dimensions.
- There may be other approaches I haven't considered. Feel free to explore your favorite.
I won't go into the calculation steps for these alternative approaches unless you need me to show them.
