Given: klmn is a trapezoid m∠n = m∠kml
me ⊥ kn , me = , ke = 8, lm: kn = 3: 5
find: km, lm, kn, area of klmn

i know that km is

The length of sides KM, LM and KN are and 16 respectively. The area of KLMN is square unit.

Step-by-step explanation:

According to given information:  KLMN is a trapezoid, ∠N= ∠KML, , ME ⊥ KN, KE=8 .

Use pythagoras theorem is triangle EKM

Let angle N and angle KML be θ.

Since angle KML and angle MKE are alternate interior angles, therefore angle MKE is θ.

In triangle KME,

    .... (1)

In triangle KNE,

.... (2)

Equate (1) and (2),

The length of side KN is

Sides LM:KN are in the ratio 3:5. Let the side lengths are 3x and 5x respectively.

The area of KLMN is

Therefore length of sides KM, LM and KN are and 16 respectively. The area of KLMN is square unit.