Answer: The area of yellow band is [tex]24x+144[/tex] sq. inches.
Step-by-step explanation:
Let the side length of the red square be 'x' inches
Width of the yellow band surrounds the red square = 6 inches
So, Length of band would be
[tex]6+x+6=x+12[/tex]
Width of band would be
[tex]6+x+6=x+12[/tex]
So, Area of the yellow band would be
[tex]\text{Area of whole band}-\text{Area of red square}\\\\=(x+12)\times (x+12)-x^2\\\\=(x+12)^2-x^2\\\\=x^2+144+24x-x^2\\\\=24x+144[/tex]
Hence, the area of yellow band is [tex]24x+144[/tex] sq. inches.
