Suppose LM ∥ KN, KL ∥ NM, h1=5, h2=6, and the perimeter of KLMN is 42. Find the area of KLMN.

210/11 square units

Step-by-step explanation:

Given that in a quadrilatral KLMN,

LM ∥ KN, KL ∥ NM, h1=5, h2=6,

and the perimeter of KLMN is 42.

Since opposite sides are given to be parallel, the quad has to be a parallelogram.

Parallelogram has sides l and w (say)

Then area of parallelogram = base x height

=l (5) = w (6) ... i

Perimeter = 2l+2w=42 ... ii

Multiply equation II by 3

6l+6w=42

Substitute for w from i

6l+5l=42

l=42/11

Area = 42/11 (5) = 210/11 square units