Math New Drill (Level 1) : Geometry (Plane figure) Problem 4 OTSUMA-2014

Quadrangular ABCD in the figure below is a parallelogram whose area is 72cm². 

AE = EF = FD = BG = GH = HC. 

Find the area of the shadow part.

Answer

8cm²

Solution

The area of parallelogram FBGD is 72 × 1/3 = 24 cm². 

As BP : PF = 2 : 1, the area of the shadow part is 24 ×1/(1+2) = 8 cm².