Question 241316: Suppose that the dimensions of a parallelogram are x yd and y yd. If they are both
multiplied by 5 , what is the area of the resulting parallelogram with these new
dimensions?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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'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 >= 0 and <= 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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