Plane α‖ plane β, △ ABC is in plane β, three lines AA ', BB', CC 'intersect at a point P, and P is between plane α and plane β, if BC = 5cm, AC = 12cm, ab = 13cm, PA': PA = 3:2, calculate the area of △ a 'B' C '

According to the meaning of the title, AB square = AC square + BC square
So triangle ABC is right angle, triangle angle ACB is right angle
Triangle ABC area = 1 / 2 * (5 * 12) = 30 square centimeters
According to the projection principle and similarity principle
A’B’=3/2AB B’c’=3/2BC A’C’=3/2AC
So triangle a'b'c'area = 3 / 2 (3 / 2) (30) = 67.5 square centimeters

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