Question
One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide.
Answers
GPT 3.5
To find the area of the shaded region, we first need to find the area of the outer rectangle and the area of the inner rectangle.
Let the length of the inner rectangle be x units and the width be y units.
The dimensions of the outer rectangle would be (x+4) units in length and (y+4) units in width.
The area of the outer rectangle is (x+4)(y+4) sq units.
The area of the inner rectangle is xy sq units.
Therefore, the area of the shaded region is:
Area of the shaded region = Area of outer rectangle - Area of inner rectangle
Area of the shaded region = (x+4)(y+4) - xy
Area of the shaded region = xy + 4x + 4y + 16 - xy
Area of the shaded region = 4x + 4y + 16 sq units
So, the area of the shaded region is 4x + 4y + 16 sq units.
Let the length of the inner rectangle be x units and the width be y units.
The dimensions of the outer rectangle would be (x+4) units in length and (y+4) units in width.
The area of the outer rectangle is (x+4)(y+4) sq units.
The area of the inner rectangle is xy sq units.
Therefore, the area of the shaded region is:
Area of the shaded region = Area of outer rectangle - Area of inner rectangle
Area of the shaded region = (x+4)(y+4) - xy
Area of the shaded region = xy + 4x + 4y + 16 - xy
Area of the shaded region = 4x + 4y + 16 sq units
So, the area of the shaded region is 4x + 4y + 16 sq units.