You can see the trapezoid in the picture I have attached. The trapezoid is shown in the picture attached.
The area of a triangle is given by the formula: A(FMN) = (b × h) / 2 = (FN × h) / 2
We can infer that KLMF is a parallelogram. Indeed: LK // MF, and LM // KF.
The area of a parallelogram is given by the formula: A(KLMF) = b × h = KF × h = 10 × h
We know that the two areas are congruent, therefore: A(KLMF) = A(FMN) FN × h / 2 = 10 × h The two heights are the same, and then cancel out FN / 2 = 10 FN = 20
Now we can calculate KN by simply adding KF and FN: KN = KF + FN = 10 + 20 = 30
