Answer:
67.5 square units
Step-by-step explanation:
Add points A, B, C, D, E and F. Note that
[tex]A_{ABCD}=A_{AMN}+A_{MBL}+A_{CKL}+A_{JKE}+A_{EDFJ}+A_{NJF}+A_{JKLMN}[/tex]
Find these area:
[tex]A_{ABCD}=AB\cdot BC=10\cdot 12=120\ un^2.\\ \\A_{AMN}=\dfrac{1}{2}AN\cdot AM=\dfrac{1}{2}\cdot 3\cdot 6=9\ un^2.\\ \\A_{MBL}=\dfrac{1}{2}MB\cdot BL=\dfrac{1}{2}\cdot 4\cdot 8=16\ un^2.\\ \\A_{CKL}=\dfrac{1}{2}CK\cdot CL=\dfrac{1}{2}\cdot 3\cdot 4=6\ un^2.\\ \\A_{JKE}=\dfrac{1}{2}EK\cdot EJ=\dfrac{1}{2}\cdot 3\cdot 1=1.5\ un^2.\\ \\A_{EDFJ}=ED\cdot EJ=4\cdot 1=4\ un^2.\\ \\A_{FJN}=\dfrac{1}{2}FN\cdot FJ=\dfrac{1}{2}\cdot 8\cdot 4=16\ un^2.[/tex]
So,
[tex]120=9+16+6+1.5+4+16+A_{JKLMN}\\ \\A_{JKLMN}=120-9-16-6-1.5-4-16=67.5\ un^2.[/tex]
