To find the area we need to do the things below:
Let:
42 = perimeter of KLMN
h1 = 5
h2 = 6
the perimeter of a parellelogram is equal to 2 (a +b)
let:
a = KL
b = LM
area of a parallelogram = bh
(also known as base x height)
b = LM
h = h1
Find the values of a and b in order to solve for the area of KLMN. Similar triangle means they are proportionality is equal.
P = 2 (a +b)
42 = 2(a+b)
12/2 = a + b
21 = a+b
21 -a = b
note:
hypotenuse / long leg
a / 5 = b/6
(21-a) / 6
a*6 = 5 (21 - a)
6a = 105 - 5a
6a + 5a = 105
11a = 105/11
= 9.55
b = 21 -a -> b = 21 - 9.55
b = 11.45
using the equation of the area of parallelogram:
area = bh
A = 11.45 * 5
A =57.25 square units
*below is an attached figure of the problem