A parallelogram has sides A, B, C, and D. Sides A and B have a length of #1 # and sides C and D have a length of # 8 #. If the angle between sides A and C is #(3 pi)/4 #, what is the area of the parallelogram?

Question

A parallelogram has sides A, B, C, and D.  Sides A and B have a length of #1  # and sides C and D have a length of # 8  #.  If the angle between sides A and C is #(3  pi)/4    #, what is the area of the parallelogram?

Ella Armstrong · Accepted Answer

Area of parallelogram is #5.6568#.

Area of a parallelogram is given by #axxbxxsintheta#, where #a# and #b# are two sides of a parallelogram and #theta# is the angle included between them. As sides are #1# and #8# and included angle is #(3pi)/4# we have #Area=1xx8xxsin(3pi)/4=8xx1/sqrt2=8x0.7071=5.6568#

Sadie Adams · Answer

undefined To find the area of the parallelogram, you can use theThe area of the parallelogram is 7 square units.To find the area of the parallelogram, you can use the formulaThe area of the parallelogram is 7 square units.To find the area of the parallelogram, you can use the formula:

Area = base * height

Since the base of the parallelogram is the length of side A (1) and the height is the perpendicular distance between side A and side C, you can find the height using trigonometry.

The height can be calculated using the formula:

height = side B * sin(angle between sides A and C)

Given that side B has a length of 1 and the angle between sides A and C is (3π)/4, you can calculate the sine of the angle.

sin((3π)/4) = √2 / 2

Now, plug in the values:

height = 1 * (√2 / 2) = √2 / 2

Now, you have the base and the height, so you can find the area:

Area = base * height
Area = 1 * (√2 / 2) = √2 / 2 square units

So, the area of the parallelogram is √2 / 2 square units.