The square with vertices (-1, -1), (1, -1), (-1, 1) and (1, 1) is cut by the line \(y=\frac{x}{2}+ 1\) into a triangle and a pentagon. What is the number of square units in the area of the pentagon? Express your answer as a decimal to the nearest hundredth.
+9466 
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
+9466
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
