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 # 1 #. 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 # 1  #.  If the angle between sides A and C is #(7  pi)/18    #, what is the area of the parallelogram?

Aurora Ayala · Accepted Answer

#color(indigo)(A_p ~~ 1.8794)# Area of a parallelogram #A_p = l * w * sin theta# #l = 2, w = 1, theta = (7pi)/18# #A_p = 2 * 1 * sin ((7pi)/18)# #color(indigo)(A_p ~~ 1.8794)#

Sophia Alfred · Answer

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

Area = base × height

In this case, the base of the parallelogram is the length of side A, which is 2 units. To find the height, we need to calculate the perpendicular distance from side A to side C.

Using trigonometry, we can find the height using the formula:

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

Substitute the given values:

height = 1 × sin((7π)/18)

Calculate the sine of the angle:

sin((7π)/18) ≈ 0.6088

Now, calculate the height:

height ≈ 0.6088

Now, calculate the area:

Area = base × height
     = 2 × 0.6088
     ≈ 1.2176

So, the area of the parallelogram is approximately 1.2176 square units.