To make a cell phone protector, a company uses plastic rectangles 6 centimeters by 10 centimeters. Then squares x centimeters wide are cut from each corner.
Use the drop-down menus below to complete statements using words and symbols to describe the area in square centimeters of the remaining plastic.
Using Words
The area of the remaining plastic is given by the difference: ________ .
Using Symbols
The area of the remaining plastic is given by the difference: ________ cm² – ________ cm².
To find the area of the remaining plastic after cutting out squares from each corner, we start with the area of the original rectangle and then subtract the area of the squares removed.
### Using Words
The area of the remaining plastic is given by the difference: the area of the original rectangle minus the total area of the squares cut from the corners.
### Using Symbols
The area of the remaining plastic is given by the difference: 60 cm² – 4x² cm².
### Explanation:
1. The area of the original rectangle is calculated as:
[
text{Area} = text{length} times text{width} = 10 text{ cm} times 6 text{ cm} = 60 text{ cm}²
]
2. Each corner has a square cut out that is (x) centimeters wide. Since there are four corners, the total area cut from the corners is:
[
text{Total area of squares} = 4 times (x times x) = 4x² text{ cm}²
]
3. Subtract the area of the squares from the area of the rectangle to find the remaining area.
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