Question

A parallelogram has sides A, B, C, and D. Sides A and B have a length of `4` and sides C and D have a length of `5`. If the angle between sides A and C is `(5 pi)/6`, what is the area of the parallelogram?

Answer 1

`10sqrt(3)" units"^2`

Explanation:

Always a good idea to draw a diagram. It helps to see what is going on!

`color(blue)("Assumption")`
`color(brown)("As the angle is presented using "picolor(white)(.)"the angle units are in Radians.")`

You can observe that if vertical lines are dropped from each end of D we have a rectangle. So the area can be determined by `"base"xx"height"`.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find h")`

Observe that `cos(pi-(5pi)/6)=h/6`

Thus `h=4cos(pi/6)->` note that `pi/6=30^o` and `cos(pi/6)=sqrt(3)/2`

`h=4xxsqrt(3)/2 = 2sqrt(3)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find area")`
Thus area `=5xx2sqrt(3)=10sqrt(3)" units"^2`

`color(brown)("Always state the units. If the type and magnitude of the units are not")` `color(brown)("known use the word 'units'.")`