<PRE><B>Question 241316</B>
area of a parallelogram = base * height.


usually you are given the height of the parallelogram and you can then find the area by multiplying the base times the height.


if x and y are the sides of the parallelogram, then the base will equal x or y.


the height will be dependent on the angle of the parallelogram.


if the angle is 90 degrees, then the height will be equal to y if the base is equal to x, or the height will be equal to x if the base is equal to y.


the formula would be:


Area of a parallelogram = x*y*sin(z) where z is the either one or the other angle of the parallelogram.


z can be either one or the other of the parallelogram because the sine of an angle is equal to the sine of it&#39;s supplement, and the opposite angles of a parallelogram are supplements of each other.


example 1:


angle  = 90 degrees
x = 15
y = 10
area = 10*15*sin(90) = 10*15*1 = 150.
area = 10*15*sin(180-90) = 10*15*sin(90) = 10*15*1 = 150


angle = 30 degrees
x = 15
y = 10
area = 10*15*sin(30) = 10*15*.5 = 75
area = 10*15*sin(180-30) = 10*15*sin(150) = 10*15*.5 = 75


angle = 80 degrees
x = 15
y = 10
area = 10*15*sin(80) = 10*15*.984807753 = 147.721163
area = 10*15*sin(180-80) = 10*15*sin(100) = 10*15*.984807753 = 147.721163


formula works for all angles of the parallelogram.
each angle of the parallelogram has to be &gt;= 0 and &lt;= 180


if the angle is 180, then the altitude is equal to 0 and the area is equal to 0.


angle = 0 degrees
x = 15
y = 10
area = 10*15*sin(0) = 10*15*0 = 0
area = 10*15*sin(180-0) = 10*15*0 = 0


if you are not given the base and the height, then you have to be given the two sides of the parallelogram and one of the angles.


your question was:


5 * x and 5 * y does what to the area.


It would multiply the area by 5 times.


instead of having x*y*sin(z), you would have 5*x*5*y*sin(z).


this would be equivalent to 25*x*y*sin(z).


that makes the area 25 times as large as x*y*sin(z).


example from above.


angle = 30 degrees
x = 15
y = 10
area = 10*15*sin(30) = 10*15*.5 = 75
area = 10*15*sin(180-30) = 10*15*sin(150) = 10*15*.5 = 75


multiply x by 5 and y by 5 and you get:


angle = 30 degrees
x = 15*5 = 75
y = 10*5 = 50
area = 75*50*sin(30) = 75*50*.5 = 1875


1875 / 75 = 25 times as large.









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