Answer:
The area of new polygon is [tex]22 x^2 + 4 x - 16[/tex].
Step-by-step explanation:
The area of square = [tex]4x^2 + 2x - 16[/tex]
Width of the rectangle = 6x+2
Length of the rectangle = x-5
Area of the rectangle = [tex](6x+2)(x-5)=6 x^2 - 28 x - 10[/tex]
Then we combined square and rectangle. The area of combined figure is the sum of area of square and rectangle.
[tex]\text{Combined area}=(4x^2 + 2x - 16)+(6 x^2 - 28 x - 10)[/tex]
On combining like terms we get
[tex]\text{Combined area}=(4x^2+6x^2)+ (2x-28x)+ (- 16- 10)[/tex]
[tex]\text{Combined area}=10x^2-26x-26[/tex]
Then, a polygon with an area of [tex]2x^2 - 30x - 10[/tex] square units is removed. So, new area of the polygon is
[tex]Area=(10x^2-26x-26)-(2x^2 - 30x - 10)[/tex]
[tex]Area=(10x^202x^2)+(-26x+30x)+(-26+10)[/tex]
[tex]Area=8 x^2 + 4 x - 16[/tex]
Therefore the area of new polygon is [tex]22 x^2 + 4 x - 16[/tex].
