A square green rug has a blue square in the center.the side length of the blue square is x inches .the width of the green band that surrounds the blue square is 6 in.What is the area of the green band?
A square red rug has a purple square in the center. The side length of the purple square is x inches. The width of the red band that surrounds the purple square is 10 in. What is the area of the red band?
To find the area of the green band, we need to subtract the area of the blue square from the area of the larger green square.
Let's calculate the side length of the larger square (green square).
The side length of the blue square is given as x inches.
The width of the green band surrounding the blue square is 6 inches on each side.
So, the side length of the green square is (x + 6 + 6) inches.
Now, let's calculate the area of the blue square.
The area of a square is given by the formula: area = side length * side length.
So, the area of the blue square is x * x = x^2 square inches.
Similarly, let's calculate the area of the green square.
The area of the green square is (side length of green square) * (side length of green square).
So, the area of the green square is (x + 6 + 6) * (x + 6 + 6) = (x + 12)^2 square inches.
Finally, to find the area of the green band, we subtract the area of the blue square from the area of the green square.
Area of green band = Area of green square - Area of blue square
= (x + 12)^2 - x^2 square inches
Simplifying this expression:
Area of green band = x^2 + 24x + 144 - x^2
= 24x + 144 square inches
So, the area of the green band is 24x + 144 square inches.
36-x^2 in.
since the square has side x, the surrounding area has side 6+x+6 = x+12
So, the green area is (x+12)^2 - x^2 = 24x+144