IMC 2004 Q7
7. Which of the following straight lines cuts the shaded area in half?
- A \(XA\)
- B \(XB\)
- C \(XC\)
- D \(XD\)
- E \(XE\)
Intermediate Mathematical Challenge 2004, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D \(XD\)
The shaded area is a trapezium of area \(\tfrac{1}{2}\)(3 + 7) × 5 = 25. Line \(XD\) forms one side of a trapezium of area 12.5, since \(\tfrac{1}{2}\)(1 + 4) × 5 = 12.5.
Solution © UK Mathematics Trust, from the IMC 2004 solutions.