Problem 23 · 2013 Math Kangaroo
Stretch
Geometry & Measurement
area-decompositiongrid-counting
A grid is drawn on a sheet of paper so that each square has sides 2 cm long. How big is the area of the grey shaded quadrilateral ABCD?
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Answer: B — 84 cm²
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Hint 1 of 2
Find the area in grid squares first, then remember each square is 2 cm by 2 cm.
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Hint 2 of 2
Use a bounding rectangle minus the corner triangles, or the shoelace idea.
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Approach: area in cells, then scale by 4 cm² per cell
- Read the corner positions of ABCD off the grid and find the enclosed area in unit cells.
- The quadrilateral covers 21 grid squares.
- Each square is 2 cm × 2 cm = 4 cm², so the area is 21 × 4 = 84 cm².
- So the area is 84 cm².
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