.
In parallelogram ABCD, AB = 13, AD = 14, and the length of diagonal AC is 15.
What is the area of the parallelogram in square units?
~~~~~~~~~~~~~~~~~
Apply the cosine law and find cosine of the angle B between the sides AB and BC of the parallelogram
(the diagonal AC is the opposite side of the triangle ABC to angle B)
AC^2 = AB^2 + BC^2 - 2*AB*BC*cos(B)
15^2 = 13^2 + 14^2 - 2*13*14*cos(B)
cos(B) = = = .
Next, find sin(B) = = = = .
Finally, find the area of the parallelogram ABCD
= AB*BC*sin(B) = = 14*12 = 168 square units. ANSWER
Solved. // An amazing phenomenon is that this answer is a precise integer number ( ! )
---------------
Another way to solve the problem is to find the area of the triangle ABC using
the Heron's formula (the lengths of the sides of the triangle are given ( ! ) ).
After finding the area of the triangle ABC simply double it,
and you will get the area of the parallelogram ABCD.