1. calculate the area of the triangular fields, and the length of perimeter fencing required to secure the site.
AB= 20m, Angle ABC= 60 degrees, Angle ACB= 20 degrees and angle BCD= 60 degrees.
Problem also cited by the OP in this thread ...
Transpositioning techniques to solve equations and Formula
You have mislabeled your diagram - angle BAC = 60, but you labeled angle CBD as 60. It also looks like you labeled angle BCA as 70 - why?
First determine angle BAC from sum of angles of triangle ABC = 180.
Then determine length |BC| using law of sines, since you know angles BAC and ACB, and length |AB|.
Now you can find lengths |AB| and |CD| from basic trig, given angles and length of the hypotenuse |BC|
Finally for triangle ABC you can use the base length of AB and height of BD to calculate its area.