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 # 4 #. If the angle between sides A and C is #(5 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 #2  # and sides C and D have a length of # 4  #.  If the angle between sides A and C is #(5  pi)/8    #, what is the area of the parallelogram?

Sadie Allen · Accepted Answer

#"area "~~7.391 # to 3 decimal places

Always start with a diagram. It helps in the understanding of what the question is asking!

Known: Area is #Cxxh#

#/_CA =5/8 pi" radians" = 5/8xx180^o = 112 1/2 " degrees"#

#color(blue)("To find h")#

#h=Asin(3/8pi) = 2sin(3/8 pi) = #

#color(blue)("To find area")#

#"area "= Cxxh= 4xx2sin(3/8 pi)#

#"area "~~7.391 # to 3 decimal places

Aaliyah Anderson · Answer

undefined The area of a parallelogram can be calculated using the formula: Area = base × height. Given the lengths of the sides and the angle between them, we can find the height of the parallelogram using trigonometry.

First, we need to find the height. Let's denote the height as h. Then, we have:
h = 2 sin((5π)/8)

Using the given values and calculating, we find:
h = 2 sin((5π)/8) ≈ 2 × 0.9239 ≈ 1.8479

Now, we can calculate the area:
Area = base × height
Area = 4 × 1.8479
Area ≈ 7.3916 square units.

Therefore, the area of the parallelogram is approximately 7.3916 square units.