Finding area of quadrilateral in Vectors

Now, we all know that every single formulas from vectors, or simply turn to that huge mind-map or thick notes we have. The other day, I asked my class the following:

All of you know how to find the area of triangle and parallelogram, but what if I want to simply find the area of a quadrilateral?

Before that, let me introduce to you all the possible quadrilaterals first, just in case.



So we are quite limited by our vectors formula here, since we might not necessary have a parallelogram! So many of them were stumped until I drew a diagonal across the quadrilaterals. And yes, if you had figures, the area of any quadrilateral will just be the sum of two triangles which we can easily find using our formulas.

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