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IMAS 2014 Junior Round 1 Question 14

IMAS · IMAS 2014 Junior Round 1

Question 14

We start with an equilateral triangle $ABC$ of area 80 cm². We construct a right isosceles triangle $BCD$ using $BC$ as the hypotenuse. Then we construct an equilateral triangle using $BD$ as a side. This continued alternately, as shown in the diagram. What is the area, in cm², of the fourth equilateral triangle?

Question illustration
  1. 1.25
  2. 5
  3. 6.4
  4. 10
  5. 40