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In the diagram, the four points have coordinates A(0,1), B(1,3), C(5,2), and D(4,0). What is the area of quadrilateral ABCD?

 

 Feb 20, 2019
 #1
avatar+17332 
+2

Here is one solution:

 Feb 20, 2019
 #2
avatar+3994 
+1

We can use the Shoelace Formula to check for the answer. 

 

Therefore, we have \(\frac{1}{2}\left|\left(0\cdot 3+1\cdot 2+5\cdot 0+4\cdot 1\right)-\left(1\cdot 1+3\cdot 5+2\cdot 4+0\cdot 0\right)\right|=\frac{1}{2}\left|6-24\right|=\frac{1}{2}\cdot 18=\boxed{9}.\)

 

Thus, I advise you to read about the shoelace formula here: https://artofproblemsolving.com/wiki/index.php/Shoelace_Theorem

 

EP is right.

 Feb 20, 2019

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