Area of triangle inside parallelogram

AI Thread Summary
To find the area of triangle PQD within a parallelogram, the user is attempting to apply the area formulas for triangles, specifically A = 1/2 ab sin(C) and Heron's formula. They express confusion about how to proceed due to the presence of multiple angles and their relationships. A suggestion is made that the angles may not be significant, as the ratios of the sides will remain consistent regardless of the angles, implying that simplifying the shape to a square could be beneficial. The discussion emphasizes the importance of understanding the relationships between the sides and angles in solving the problem.
cjwalle
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Homework Statement



http://folk.uio.no/robinbj/gg/ggstart.pdf"
I am supposed to find the area of the triangle PQD. The numbers given are the areas of the other triangles.

Homework Equations


A= \frac{1}{2} a b \sin{C}

As well as Heron's formula, possibly?
A= \sqrt{s(s-a)(s-b)(s-c)} where s = \frac{a+b+c}{2}

The Attempt at a Solution


Where I'm stumped is exactly how to start. At first, I figured I'd try to find the values of a, b and c. Using the area of a triangle:

a = DP = \frac{14}{AP\sin{\theta}}

Similarly, for b:

b = QP = \frac{56}{QB\sin{\alpha}}

And c:

c = QD = \frac{28}{QC\sin{x}}

Meaning that s = \frac{7}{AP\sin{\theta}} + \frac{28}{QB\sin{\alpha}} + \frac{14}{QC\sin{x}}

However, dealing with three different angles, without knowing the relationship between them or the sum of the angles, I just don't know how to proceed and solve the exercise based on this. I am not looking for a solution from you guys, mind you. Just a tip to get me on the right track?

Thank you.
 
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Hi cjwalle! :smile:

I don't think the angles matter …

won't the ratios be the same, whatever the angles are, so you might as well make it a square?
 
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