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# Find the area of the region determined by the system ​

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Find the area of the region determined by the system \begin{align*} y &\geq |x| \\ y &\leq -|x+1| + 4. \end{align*}

waffles  Mar 15, 2018
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This area forms a rectangle with vertices  (0,0), (1.5,1.5), (-1,4)  and (-2.5, 2.5)

The length of one side is  √ [2 * 1.5^2 ] =  1.5√2

And the length of the other side is √ [2 *2.5^2 ]  = 2.5√2

So  the total area  = 1.5√2 * 2.5√2  =  3.75 * 2    =  7 units^2

Here's a pic of the region :  https://www.desmos.com/calculator/zlpwagi3cx

CPhill  Mar 15, 2018