Since all the measurements are whole numbers, we can easily solve the problem by guessing, knowing that the side lengths of right triangles KMN and KML are Pythagorean triples.
Since MN=13, KN is almost certainly either 5 or 12. Trying KN=5 makes MK=12 and LM=9; and that makes triangle KML a Pythagorean triple 9, 12, and 15.
So triangle KMN is a 5-12-13 triangle with area (5*12)/2 = 30; triangle KML is a 9-12-15 triangle with area (9*12)/2 = 54.
Then the area of KLMN is 30+54 = 84.
The problem can be solved formally using the Pythagorean Theorem.
Let KN = x; then LM = x+4. And let KM = y. Then
Then the rest of the path to the answer to the question is the same as above.
