in figure LM = 18 ft, KM=16 ft and KN=14ft what is the area of KLM

Answer 1

Was that supposed to say KL = 14 ?

I will assume that, since N does not enter the picture elsewhere.

Let's find angle K, the largest angle.

18^2 = 14^2 + 16^2 - 2(14)(16)cosK
448cosK = 128
cosK = 2/7
K = appr 73.4°

area = (1/2)(14)(16)sinK
= 112(.9583..)
= appr 107.33 ft^2

for "exact value" :
If cosK = 2/7, then sinK = √(1 - 4/49)
= √45/7

area = (1/2)(14)(16)(√45/7)
= 16√45
which is appr 107.33.. , just like above