Problem 25 · 2018 Math Kangaroo
Stretch
Geometry & Measurement
areasymmetry
Lisa’s aviation club designs a flag with a flying “dove” on a 4×6 grid. The area of the “dove” is 192 cm². The perimeter of the “dove” is made up of straight lines and circular arcs. What measurements does the flag have?
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Answer: D — 24 cm x 16 cm
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Hint 1 of 2
By the design's symmetry the dove covers exactly half of the whole grid.
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Hint 2 of 2
Find the total grid area, then the area of one of the 4×6 cells to get the cell side.
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Approach: dove = half the grid, then size one cell
- The dove's curved and straight pieces fit so it fills exactly half the grid, so the grid area is 2 · 192 = 384 cm².
- The grid has 4 · 6 = 24 equal cells, so each cell is 384 : 24 = 16 cm², i.e. 4 cm by 4 cm.
- The flag therefore measures 6 · 4 by 4 · 4 = 24 cm × 16 cm.
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