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

Answer 1

`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!")`

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.

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`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

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`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