Question

Given: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMN

Answer 1

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