GK 2017 Q14
14. Two segments, each 1 cm long, are marked on opposite sides of a square of side 8 cm. The ends of the segments are joined as shown in the diagram. What is the total shaded area?
- A 2 cm2
- B 4 cm2
- C 6.4 cm2
- D 8 cm2
- E 10 cm2
Grey Kangaroo 2017, Question 14. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 4 cm2
Let the height of the lower triangle be \(h\) cm. Therefore the height of the upper triangle is \((8 - h)\) cm. Hence the shaded area in cm2 is \(\tfrac{1}{2} \times 1 \times h + \tfrac{1}{2} \times 1 \times (8 - h) = \tfrac{1}{2} \times (h + 8 - h) = 4\).
Solution © UK Mathematics Trust, from the GK 2017 solutions.