Question 1154678
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Breaking the figure into three triangles and finding the area of each is an astonishingly bad (and tedious!) way to try to get the answer...!<br>
The matrix method for solving the problem, used by a couple of the other tutors, is clearly the easiest way to get the answer.  But the method suggested by another tutor of inscribing the given figure in a rectangle is also an easy method.<br>
I will steal another tutor's figure and add to it to find the answer by this method.<br>
{{{drawing( 600, 600, -10, 15, -10, 15,
circle(0,0,.14), locate(0.3,1,A),
circle(0,4,.13), locate(0.3,4,B),
circle(8,8,.13), locate(8.3,9,C),
circle(14,0,.13), locate(14.3,1,D),
circle(9,-2,.13), locate(9.3,-2.5,E),
green(line(0,4,8,8)),green(line(0,0,9,-2)),green(line(9,-2,14,0)),green(line(14,0,8,8)),
blue(line(0,0,0,8)),blue(line(0,8,14,8)),blue(line(14,8,14,-2)),blue(line(14,-2,0,-2)),
locate(.2,9,P),locate(14.2,8,Q),locate(14.2,-2,R),locate(.2,-2.5,S),
 graph( 600, 600, -10, 15, -10, 15, 0)) }}}<br>
The area of rectangle PQRS (dimensions 14x10) is 140.<br>
The area of right triangle BPC (legs 4 and 8) is 16
The area of right triangle CQD (legs 6 and 8) is 24
The area of right triangle DRE (legs 2 and 5) is 5
The area of right triangle ESA (legs 2 and 9) is 9<br>
The area of polygon ABCDE is 140-(16+24+5+9) 140-54 = 86.<br>