GK 2020 Q2
2. A large square is divided into smaller squares. In one of the smaller squares a diagonal is also drawn, as shown. What fraction of the large square is shaded?
- A \(\tfrac{4}{5}\)
- B \(\tfrac{3}{8}\)
- C \(\tfrac{4}{9}\)
- D \(\tfrac{1}{3}\)
- E \(\tfrac{1}{2}\)
Grey Kangaroo 2020, Question 2. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E \(\tfrac{1}{2}\)
The shaded square in the lower right corner of the large square is \(\tfrac{1}{4}\) of the large square. The shaded triangle is half of \(\tfrac{1}{4}\) of the large square. Hence it is \(\tfrac{1}{8}\) of the large square. The two small shaded squares in the upper left corner together are half of \(\tfrac{1}{4}\), or \(\tfrac{1}{8}\), of the large square. Therefore the fraction of the large square that is shaded is \(\tfrac{1}{4} + \tfrac{1}{8} + \tfrac{1}{8} = \tfrac{1}{2}\).
Solution © UK Mathematics Trust, from the GK 2020 solutions.