GK 2019 Q15
15. Some identical rectangles are drawn on the floor. A triangle of base 10 cm and height 6 cm is drawn over them, as shown, and the region inside the rectangles and outside the triangle is shaded. What is the area of the shaded region?
- A 10 cm2
- B 12 cm2
- C 14 cm2
- D 15 cm2
- E 21 cm2
Grey Kangaroo 2019, Question 15. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 12 cm2
Since the length of five identical rectangles is 10 cm, the length of one rectangle is 2 cm. Similarly, since the height of four rectangles is 6 cm, the height of one rectangle is 1.5 cm. Therefore the total area of the 14 rectangles is 14 × (2 × 1.5) cm2 = 42 cm2. Hence the area of the shaded region is equal to \(\left(42 - \tfrac{1}{2} \times 10 \times 6\right)\) cm2 = (42 − 30) cm2 = 12 cm2.
Solution © UK Mathematics Trust, from the GK 2019 solutions.