A parallelogram has sides A, B, C, and D. Sides A and B have a length of #9 # and sides C and D have a length of # 8 #. If the angle between sides A and C is #(5 pi)/12 #, 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 #9  # and sides C and D have a length of # 8 #.  If the angle between sides A and C is #(5  pi)/12    #, what is the area of the parallelogram?

James Atkins · Accepted Answer

Area is #69.5448# Area of a parallelogram whose two sides are #x# and #y# and angle between them is #theta# is given by #x xx yxxsintheta#. Hence area is #9xx8xxsin((5pi)/12)=72xx0.9659=69.5448#

Maverick Smith · Answer

undefined To find the area of the parallelogram, you can use the formula: Area = base * height. The base of the parallelogram is the length of either side A or side C, and the height is the perpendicular distance between side A and side C.

Given that side A has a length of 9 and the angle between sides A and C is $ \frac{5\pi}{12} $, you can use trigonometry to find the height. The height can be calculated as: height = side A * sin(angle between A and C).

height = 9 * sin($ \frac{5\pi}{12} $).

Using the given values, calculate the height.

Then, once you have the height, you can find the area using the formula: Area = base * height, where the base is 9.

Calculate the area using the obtained height.