MathDB

Csenge has a yellow and a red foil on her rectangular window which look beautiful in the morning light. Where the two foils overlap, they look orange. The window is

80

cm tall,

120

cm wide and its corners are denoted by

A, B, C

and

D

in the figure. The two foils are triangular and both have two of their vertices at the two bottom corners of the window, A and

B

. The third vertex of the yellow foil is

S

, the trisecting point of side

DC

closer to

D

, whereas the third vertex of the red foil is

P

, which is one fourth on the way on segment

SC

, closer to

C

. The red region (i.e. triangle

BPE

) is of area

16

^2

. What is the total area of the regions not covered by foil? https://cdn.artofproblemsolving.com/attachments/b/c/ea371aeafde6968506da6f3456e88fa0bddc6d.png

Problem Statement