In parallelogram ABCD, AB=125cm, AD=132cm, and the length of diagonal AC is 32cm. The area of the parallelogram, in cm2, is
+128406 Since we have a parallelogram.....
AB = DC = 125
We can find the cosine of angle ADC with the Law of Cosines
AC^2 = AD^2 + DC^2 cos ( ADC)
32^2 = 132^2 + 125^2 - 2 ( 132 * 125) cos (ADC)
[ 32^2 - 132^2 - 125^2 ] / [ -2 * 132 * 125 ] = cos ADC = 427/440
sin ADC = sqrt [ 1 - (427/440)^2 ] = (17/440)sqrt (39)
The area is
AD * DC sin ADC =
132 * 125 * ( 17/440) sqrt(39) ≈ 3981.19 cm^2
