IMC 2005 Q9
9. Which of the following shaded regions has an area different from the other shaded regions?
Intermediate Mathematical Challenge 2005, Question 9. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D
The area of triangle A = \(\tfrac{1}{2}\) × 2 × 3 = 3; the area of parallelogram B = 1 × 3 = 3; the area of triangle C = \(\tfrac{1}{2}\) × 3 × 2 = 3; the area of rectangle E = 1 × 3 = 3. However, the area of triangle D = 3 × 3 − (3 + 3 + \(\tfrac{1}{2}\)) = 2\(\tfrac{1}{2}\).
Solution © UK Mathematics Trust, from the IMC 2005 solutions.