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What is the area of the triangle whose vertices are D(−7, 3) , E(−7, 9) , and F(−11, 7) ? Enter your answer in the box. units²

 Jan 6, 2018

Here is a diagram for you to reference as I solve for the area of the triangle. Notice that I added \(\overline{FG}\) such that the segment is the altitude of the triangle.



Since the altitude and base of this triangle lie on gridlines, we can simply count the distance (as opposed to using the distance formula).


\(ED=6\\ FG=4\)


We already have all the information needed to solve for the area. Just use the area formula for a triangle, A=1/2*bh.


\(A_{\triangle DEF}=\frac{1}{2}ED*FG\)We already know the values of ED and FG, so let's plug them in!
\(A_{\triangle DEF}=\frac{1}{2}*6*4\)Now, we simplify. multiplying 6 by 1/2 eliminate the fraction, but you can multiply in any order you'd like.
\(A_{\triangle DEF}=3*4\) 
\(A_{\triangle DEF}=12\text{units}^2\) 
 Jan 6, 2018

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