Answer:
Area of red band is [tex](20x + 100) inch^{2}[/tex]
Step-by-step explanation:
We know that area of square = [tex]side^{2}[/tex]
Please refer to the attached figure, we have to calculate the area of red band.
Required area = Area of square ABCD - Area of purple square
Side of purple square = [tex]x[/tex]
So, area of purple square = [tex]x^{2}[/tex]
ABCD is a square with purple square at the center and there is symmetry in the figure.
So, width of red band towards both the end is 5 inches.
[tex]\Rightarrow \text{side of }ABCD = 5 + 5 +x = (x+10) inches[/tex]
Required area = [tex](x+10)^{2} - x^{2}[/tex]
Using formula [tex]a^{2} - b^{2} = (a-b)\times (a+b)[/tex]
[tex]\Rightarrow (x+10-x)(x+10+x)\\\Rightarrow (10)(2x+10)\\\Rightarrow (20x+100)[/tex]
Hence, Area of red band is [tex](20x + 100) inch^{2}[/tex]
