Question 1186474
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Here is a partial diagram of the figure....<br>
{{{drawing(400,400,-2,12,-2,12
,line(0,0,10,0),line(10,0,10,10),line(10,10,0,10),line(0,10,0,0)
,line(2,2,8,2),line(8,2,8,8),line(8,8,2,8),line(2,8,2,2)
,line(5,5,5,10),line(2,8,0,10),line(8,8,10,10)
,locate(0,-.25,A),locate(10,-.25,B),locate(10,10.75,C),locate(0,10.75,D)
,locate(2,1.75,P),locate(8,1.75,Q),locate(8,8.75,R),locate(2,8.75,S)
,locate(5,10.75,10),locate(5.25,9.5,"(x)"),locate(5.25,6.5,"(5-x)")
,locate(3,8.75,"(5-x)"),locate(6,8.75,"(5-x")
)}}}<br>
The area of trapezoid SRCD is 16:<br>
{{{A = h((b(1)+b(2))/2)}}}<br>
{{{16 = x((10+10-2x)/2)}}}
{{{16 = x(10-x)}}}
{{{16 = 10x-x^2}}}
{{{x^2-10x+16=0}}}
{{{(x-2)(x-8)=0}}}<br>
{{{x=2}}} or {{{x=8}}}<br>
Obviously from the diagram the x we want is x=2.<br>
ANSWER: the height of the trapezoid is 2cm.<br><hr>
NOTE: The solution from tutor @ikleyn, using the fact that the four trapezoids are congruent, is much easier than my solution above....<br>