Problem 5 · 2016 Math Kangaroo
Easy
Geometry & Measurement
areaarea-fraction
Kathi draws a square with side length 10 cm. Then she joins the midpoints of each side to form a smaller square. What is the area of the smaller square?
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Answer: E — 50 cm²
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Hint 1 of 3
Connecting the midpoints leaves a tilted square inside, with a small triangle at each corner.
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Hint 2 of 3
Picture sliding the four corner triangles inward; they exactly fill the tilted square.
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Hint 3 of 3
So the inner square is half of the big square.
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Approach: the midpoint square is half the original
- Joining the midpoints cuts off four equal right triangles, one at each corner of the big square.
- Those four triangles are the same size as the four triangles that make up the tilted inner square, so the inner square is exactly half of the big square.
- The big square has area \(10 \times 10 = 100\), so the inner square is half of that, \(50\text{ cm}^2\), choice (E).
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