If an 8" by 10" photo is surrounded by a 2" wide picture frame, what is the area of the picture frame?

This classic geometry problem contains a common trap: forgetting that a two-inch frame adds two inches to *every* side. This means the overall width and height of the entire piece each increase by a total of four inches, not just two. Understanding this is the key to finding the correct area for the border.

To solve this, we must first calculate the total area of the photo and the frame together as one large rectangle. The original 8-inch side gets a 2-inch border on its left and right, making the new width 12 inches (8 + 2 + 2). Likewise, the 10-inch side gets a 2-inch border on its top and bottom, for a new total height of 14 inches (10 + 2 + 2). Multiplying these new outer dimensions (12 x 14) gives us a total area of 168 square inches.

The final step is to subtract the area of the part we don't want to include, which is the photo itself. The photo's area is 80 square inches (8 x 10). By taking the total area of 168 and subtracting the photo's area of 80, we are left with the 88 square inches that make up the frame. This "area of a border" calculation is a practical skill used in fields from construction to landscaping.