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area of pentagon   =   area of square - area of triangle

area of square   =   (side length)²   =   2²   =   4

To find the area of the triangle, we need to find the coordinates of  A  and  B .

To find point  A , we need to find the y-coordinate of the line when  x = -1 .

$y\ =\ \frac{x}{2}+1\\~\\y\ =\ \frac{-1}{2}+1\\~\\y\ =\ \frac12$

So   A  =  (-1, $\frac12$)

To find point  B , we need to find the x-coordinate of the line when  y = 1 .

$y\ =\ \frac{x}{2}+1\\~\\ 1\ =\ \frac{x}{2}+1\\~\\ 0\ =\ \frac{x}{2}\\~\\ 0\ =\ x$

So   B  =  (0, 1)

base of triangle   =   0 - -1   =   1

height of triangle  =  1 - $\frac12$   =   $\frac12$

area of triangle   =   $\frac12$( base )( height )   =   $\frac12$( 1 )( $\frac12$ )   =   $\frac14$

Now we can find the area of the pentagon.

area of pentagon   =   area of square - area of triangle   =   4 - $\frac14$   =   3.75

Here's the graph:  https://www.desmos.com/calculator/prypeui4fb