In the figure, each pair of consecutive sides forms a right angle.  What is the area of the figure?

[asy]
draw((6,0)--(13.5,0));
label("9''",(9.75,0),S);
draw((6,0)--(6,3));
label("4''",(6,1.5),W);
draw((6,3)--(0,3));
label("8''",(3,3),S);
draw((0,3)--(0,9));
label("7''",(0,6),W);
draw((0,9)--(9,9));
label("12''",(4.5,9),N);
draw((9,9)--(9,6.75));
label("3''",(9,7.625),E);
draw((9,6.75)--(13.5,6.75));
draw((13.5,6.75)--(13.5,0));
[/asy]
[asy]
defaultpen(linewidth(.8));
draw((2,0)--(0,0)--(0,1),dashed);
draw((0,1)--(0,2.75)--(3,2.75));
draw((3,2.75)--(4.25,2.75)--(4.25,2),dashed);
draw((3,2.75)--(3,2)--(4.25,2)--(4.25,0)--(2,0)--(2,1)--(0,1));
label("7''",(0,1.875),E);
label("12''",(1.5,2.75),N);
label("3''",(3,2.375),E);
label("8''",(1,1),S);
label("4''",(2,.5),W);
label("9''",(3.125,0),N);
label("5''",(3.75,2),N);
[/asy]

Notice that there are two rectangular holes in the top right corner and the bottom left corner. If these holes were filled, the entire figure would be a rectangle with length $8+9=17$ inches and width $7+4=11$ inches. The area would be $17\cdot11=187$ square inches. The area of the top right hole is $5\cdot3=15$ square inches and the area of the bottom left hole is $8\cdot4=32$ square inches. The area of the given figure is the area of the large rectangle minus the areas of the two holes, or $187-15-32=\boxed{140}$ square inches.