New Math Drill : Level 1 : Geometry(Plane figure) Problem2(6) JISSENJOSHIGAKUEN-2014

What cm² is the shadow area of the figure below?

Answer

24 cm²

Solution

(Shadow area) = (Triangle DBC) - (Triangle HBE) - (Triangle DGF). 

△ AHD and△ HBE are homothetic and the homothetic ratio is 12 : 6 = 2 : 1. 

Since the base of △ HBE = 6 cm and the height = 6 × 1/(1 + 2) = 2 cm, the area is 6 × 2/2 = 6 cm². 

△ ABG and△ DGF are homothetic and the homothetic ratio is 6 : 3 = 2 : 1. 

Since the base of △DGF = 3 cm and the height= 12 × 1/(1 + 2) = 4 cm, the area is 3 × 4 / 2 = 6 cm². 

Therefore the shadow area = 12 × 6 / 2 - 6 - 6 = 36 - 12 = 24 cm².