Problem 25 · 2021 Math Kangaroo
Stretch
Geometry & Measurement
areapythagorean-triple
The smaller square in the picture has area 16 and the grey triangle has area 1. What is the area of the larger square, in cm²?
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Answer: B — 18
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Hint 1 of 2
The smaller square has side 4; the larger tilted square's side is the hypotenuse of a small right triangle.
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Hint 2 of 2
Use the grey triangle's area 1 to find that triangle's legs, then the larger side squared by Pythagoras.
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Approach: larger area via the corner right triangle
- The smaller square has side 4. The larger square's side is the slanted segment forming a right triangle at the corner.
- The grey triangle has area 1, fixing the small offset between the squares.
- Adding the squared legs (Pythagoras) gives the larger square's area as 16 + 2 = 18.
- The larger square's area is 18 cm², choice (B).
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