##205.9sq.cm##
Area of trapezium=##1/2(a+b)h=((a+b)h)/2##
Where ##a and b=parall####e####l## ##sidesh=height##
Now in an isoceles trapezium the legs are equal and in this case they are in a length of ##13##
Now consider the diagram:
Now we will have a short sypnosis of the lengths:
##ab=23fd=12dp=fs=h##
Now we need to find the height:In this case the height is in a right triangle.Sowe use the :
##a^2+b^2=c^2##
Where ##a## and ##b## are the two adjacent sides##c=hypoten####use## (longest side)
But we should know the length of ##pb## to know the height:
##rarrpb=(23-12)/2=11/2=5.5##
We divide it by ##2## because there is another side as ##as## which equals ##pb## :
So
##rarrh^2+5.5^2=13^2##
##rarrh^2+30.25=169##
##rarrh^2=169-30.25##
##rarrh^2=138.75##
##rarrh=sqrt138.25=11.77##
Now
##Area=((23+12)11.77)/2##
##rarr=((35)11.77)/2##
##rarr=411.9/2=205.95sq.cm^2##
If we round it off to the nearest tenths we get ##205.9sq.cm^2##