Step-by-step explanation:
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the first thing we notice : the quadrilateral has 2 pairs of equally long sides with 2 angles being openly 90°.
so, we are dealing with a rectangle here.
we know that one pair of the sides (NK = LM) are 24 cm long.
and we know that KL:LM = 3:4.
that means that the pair KL = MN are the shorter sides of the rectangle. and their length is according to the ratio 3/4 of NK=LM.
3/4 × 24 = 18 cm
the area of that rectangle is therefore
18 × 24 = 432 cm²
