A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 6 #. If the angle between sides A and C is #(7 pi)/18 #, 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 #2  # and sides C and D have a length of # 6  #.  If the angle between sides A and C is #(7  pi)/18    #, what is the area of the parallelogram?

Savannah Aguilar · Accepted Answer

12

The area of a parallelogram is given by #A=bh#, where #b# is the base length and #h# is the height. #A=bh# #A=(2)(6)# #A=12# Therefore, the area of the parallelogram is 12 square units.

Sadie Allen · Answer

undefined The area of the parallelogram can be calculated using the formula:

$$ \text{Area} = \text{Base} \times \text{Height} $$

where the base is the length of one of the sides, and the height is the perpendicular distance between the base and its opposite side.

Given that sides A and C are adjacent sides of the parallelogram, the length of side A is 2, and the angle between sides A and C is $ \frac{7\pi}{18} $, the height of the parallelogram can be found using the sine of the angle.

$$ \text{Height} = \text{Side A} \times \sin(\text{angle}) $$

$$ \text{Height} = 2 \times \sin\left(\frac{7\pi}{18}\right) $$

Once the height is found, the area can be calculated as:

$$ \text{Area} = \text{Base} \times \text{Height} $$

$$ \text{Area} = 6 \times \left(2 \times \sin\left(\frac{7\pi}{18}\right)\right) $$

$$ \text{Area} = 12 \times \sin\left(\frac{7\pi}{18}\right) $$