Take a look at triangle OFG, whose hypotenuse is 13 and whose longer side is 12. Its shorter side is 5, via the Pythagorean Theorem. Thus, the width of the trapezoid is 5.
Then the area of the trapezoid is
A = (average of the lengths of the trapezoid)(width of trapezoid)
30+ 40
= -------------- * 5 = 35*5= 175 square units.
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