A parallelogram has sides A, B, C, and D. Sides A and B have a length of #6 # and sides C and D have a length of # 3 #. If the angle between sides A and C is #(3 pi)/8 #, 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 #6  # and sides C and D have a length of # 3  #.  If the angle between sides A and C is #(3  pi)/8    #, what is the area of the parallelogram?

Autumn Armstrong · Accepted Answer

The area of the parallelogram is # 16.63 # sq.unit.

The adjacent sides of the parallelogram are #s_1=6# unit and #s_2=3# unit and angle between them #theta =(3 pi)/8# or #theta=(3 *180)/8 =67.5^0# We know the area of the parallelogram as #A_p=s_1*s_2*sin theta # or #A_p=6* 3 *sin 67.5 ~~ 16.63 # sq.unit. The area of the parallelogram is # 16.63 # sq.unit.[Ans]

Sadie Allen · Answer

undefined To find the area of the parallelogram, you can use the formula:

$$ \text{Area} = \text{base} \times \text{height} $$

In a parallelogram, the height is the perpendicular distance between the pair of parallel sides. You can find the height by using trigonometry since you have the length of one side and the angle between the sides.

Given:
- Length of side A (base) = 6
- Angle between sides A and C = $ \frac{3\pi}{8} $

You can find the height using the sine of the given angle:

$$ \sin\left(\frac{3\pi}{8}\right) = \frac{\text{height}}{6} $$

Solve for the height:

$$ \text{height} = 6 \times \sin\left(\frac{3\pi}{8}\right) $$

Once you have the height, you can calculate the area using the formula mentioned earlier:

$$ \text{Area} = 6 \times \text{height} $$

Now, calculate the height and then use it to find the area of the parallelogram.