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.

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) (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.

$$$

RELATED QUESTIONS
The legnths of two adjacent sides of a parallelogram are 6 and 15. If the measure of an... (answered by ankor@dixie-net.com)

Two adjacent side of a parallelogram are 10 and 8 in. The included angle is 30 degrees.... (answered by FrankM)

One angle of a parallelogram is 120 degrees,and two consecutive sides have lengths of 8... (answered by Tatiana_Stebko,Edwin McCravy)

The sides of a parallelogram have lengths 8 inches and 16 inches and one of the angles of (answered by checkley75)

what is the area of a parallelogram whose sides are 20 inches and 45 inches one of the... (answered by stanbon)

Find the length of the longer diagonal of a parallelogram two of whose sides are 34mm and (answered by Edwin McCravy)

Parallelogram ABCD has one interior angle measuring 60�. What is the measure of the... (answered by jim_thompson5910)

Find the area of a parallelogram with sides 10 feet and 40 feet and an included angle of... (answered by hokies)

The sides of a parallelogram measure 10 cm and 18 cm. One angle of the parallelogram... (answered by Gogonati)