suppose you are framing a 3 by 5 in rectangular picture with a frame that is w inches wide all around. What is the area of the picture frame
since there is a border of w on both sides and both ends, the total area is
(3+2w)(5+2w) - 3*5
To find the area of the picture frame, we need to subtract the area of the picture from the area of the outer rectangle formed by the frame.
1. Let's first calculate the area of the outer rectangle:
- The length of the outer rectangle would be the length of the picture plus twice the width of the frame, since there are two sides of the frame on each side of the picture.
- The width of the outer rectangle would be the width of the picture plus twice the width of the frame, for the same reason mentioned above.
- Therefore, the length of the outer rectangle would be 3 + 2w inches, and the width of the outer rectangle would be 5 + 2w inches.
2. Next, calculate the area of the picture:
- The area of the picture is simply the length multiplied by the width, which is 3 inches multiplied by 5 inches, giving us 15 square inches:
3. Finally, subtract the area of the picture from the area of the outer rectangle:
- The area of the picture frame would be the area of the outer rectangle minus the area of the picture, which is:
(3 + 2w) inches * (5 + 2w) inches - 15 square inches.
This is the step-by-step process to calculate the area of the picture frame.
To find the area of the picture frame, we need to subtract the area of the picture from the area of the framed picture.
First, let's find the area of the picture:
The picture is a rectangle with dimensions 3 inches by 5 inches. So the area of the picture is 3 inches multiplied by 5 inches, which gives us 15 square inches.
Now, let's find the dimensions of the framed picture:
If the frame is w inches wide all around, then the dimensions of the framed picture will be increased by 2w inches in both the length and width.
The length of the framed picture will be 3 inches + 2w inches + 2w inches, which simplifies to 3 inches + 4w inches.
The width of the framed picture will be 5 inches + 2w inches + 2w inches, which simplifies to 5 inches + 4w inches.
The area of the framed picture will then be (3 inches + 4w inches) multiplied by (5 inches + 4w inches).
Finally, we can find the area of the picture frame by subtracting the area of the picture from the area of the framed picture:
Area of the picture frame = Area of the framed picture - Area of the picture
Area of the picture frame = (3 inches + 4w inches) multiplied by (5 inches + 4w inches) - 15 square inches
This equation gives us the area of the picture frame in square inches.