SOLUTION: The adjacent sides of a parallelogram measure 8 by 6 inches. Their included angle is 45 Degrees. What is the area of the parallelogram.

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Question 936536: The adjacent sides of a parallelogram measure 8 by 6 inches. Their included angle is 45 Degrees. What is the area of the parallelogram.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your parallelogram is ABCD
AB is equal to 8
BC is equal to 6
your 45 degree angle is angle ABC

drop a perpendicular from B to intersect with the extension of CD at E.
the angle ABE is a right angle.
the angle BEC is a right angle.

angle CBE is complement to angle ABC and is therefore equal to 90 - 45 = 45.

cos(CBE) = adjacent / hypotenuse = BE / BC

the length of BE is equal to x.
the length of BC is equal to 6.

cos(CBE) = cos(45) = x / 6

solve for x to get x = 6 * cos(45) which makes x = 6 * sqrt(2) / 2 which makes x = 3 * sqrt(2) which is equal to 4.242640687.

area of the parallelogram is equal to base * height which is equal to 8 * sqrt(2) / 3 which is equal to 8 * 4.242640687 which is equal to 33.9411255.

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