We have a right trapezoid since ∠K=90°. We know that KL=LM, then the triangle KLM is an isosceles and according to the Pythagoras theorem KM = 10√2.
The sum of all quadrilaterals is 360° and using this fact we can say that ∠LMN=135° and since we know that ΔKLM is an isosceles( ∠LMK=45°), ∠KMN=90° and since ∠MNK=45°, then ∠MKN=45°. It means triangle KMN is a right-isosceles triangle and KM=MN=10√2. According to Pythagoras theorem KN=20
And the area of the trapezoid is [tex]A= \frac{10+20}{2}10=150 [/tex]
