Given curves are y=|x−1| and y=3−|x|. The intersection point of lines x+y=1 and y−x=3 is B(−1,2). and intersection point of lines x−y=1 and y=3−x is D(2,1)
Now, Area of △ACE=
1
2
×AE×OC=
1
2
×6×3=9 Area of △ABF=
1
2
×AF×BG=
1
2
×4×2=4 and Area of △FDE=
1
2
×EF×DH=
1
2
×2×1=1 ∴ Required shaded region = Area of △ACE - Area of △ABF - Area of △FDE =9−4−1=4 sq units