Question

Iven: KLMN is a trapezoid
m∠K = 90°, m∠N = 45°
LK = LM = 10
Find: KN, Area of KLMN

Answer 1

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
`A= (10+20)/(2)10=150`