colorful illustration of a large number three submerged in the ground, creating a reflection
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Reflections

We define triangle ABC with area 30. We use point reflection to create A’ by reflecting A over B. Similarly, we reflect point B over C, giving us B’. Finally, we reflect point C over A, giving us C’

Challenger

reflections

Calculate the area of triangle A’B’C’. Round your answer to the nearest whole number. Attention: the figure is not drawn to scale.

Mastermind

double reflections

We now also reflect A over C (A’’), B over A (B’’), and C over B (C’’). Calculate the area of the star formed by the partially overlapping triangles A’B’C’ and A’’B’’C’’. Round your answer to the nearest whole number. Attention: the figure is not drawn to scale.