Question 84019
*I would assume that this problem involves the use of trigonometry. I was not sure so I am offering a solution without trigonometry. If it actually involves trig, I can offer another solution.

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• Draw a tidy diagram of this problem. Label what you know.

• Denote the intersection of angles (perpendicular bisector in parallelograms) any letter you want. I'll call it O.

• A parallelogram's area = Base x Height. However, height is not given here. 

• We can also find area by another way. Twice the area of the triangles formed by the diagonals = the area of the parallelogram. 

So, the area of the parallelogram = Area of triangles ACD + ABD or Area of triangles BDC + BAC (either set works).


I'll stick with ACD + ABD:, so all you need to do is calculate the area of either ACD or ABD. I'll pick ACD. 

You know AD is the base, but you don't know the height. However, O is perpendicular so triangle COD is a right angle triangle. You have CD = 10 and AD = 4sqrt(3). Use the Pythagoras Theorem to find out OC, which is rounded to 9.38.

So now you know triangle ACD's area = 4sqrt(3) x 9.38 

                                    = 64.987 

So double that, and you get 129.974 sq. units, which is area of the entire parallelogram.