Problem 18 · 2010 Math Kangaroo
Hard
Geometry & Measurement
area-decomposition
What fraction of the square is grey?
Show answer
Answer: A — \(\tfrac{1}{3}\)
Show hints
Hint 1 of 2
The square is \(6 \times 6\), since each side is \(2 + 4\); find its area first.
Still stuck? Show hint 2 →
Hint 2 of 2
Instead of the grey shape, find the two white right triangles and take them away from the whole square.
Show solution
Approach: whole square minus the two white triangles
- Each side of the square is \(2 + 4 = 6\), so the whole square is \(6 \times 6 = 36\).
- The two white right triangles each have legs 4 and 6, so each is \(\tfrac{1}{2} \times 4 \times 6 = 12\), giving \(24\) white in all.
- The grey part is \(36 - 24 = 12\), and \(\tfrac{12}{36} = \tfrac{1}{3}\) — the answer is A.
Mark:
· log in to save