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 # 3 #. If the angle between sides A and C is #(5 pi)/8 #, what is the area of the parallelogram?

1 Answer
Tony B
Feb 25, 2016

#color(blue)("Approximate area "5.54" units"^2" "# to 2 decimal places

Explanation:

#color(blue)("Always good to draw a diagram. You can see what you are dealing with then!")#

Tony B

The thing about parallelograms is the if you cut of the left hand side triangle and glued it back onto the right hand side you would have a rectangle. The area of a rectangle is (length of base #xx# length of height). That is exactly what we are going to do.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To find height")#

Looking at the triangle we have #h=3xxcos(pi/8) =3xxcos(22 1/2^o)#

#h~=2.772# to 2 decimal places

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

Precise value #2xx3cos(pi/8)" "=" " 6cos(pi/8) "units"^2#

#color(blue)("Approximate area "5.54" units"^2" "# to 2 decimal places

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