Final answer:
To calculate the painted surface area of the cabinet, you find the area of each side except the back and sum them up, which results in 83 square feet.
Step-by-step explanation:
The surface area of the cabinet that is being painted is calculated by finding the area of each side and adding them together while excluding the back side. The cabinet has a height of 7 feet, a width of 4 feet, and a length of 2.5 feet. We calculate the surface area for each side as follows:
The surface area of the cabinet that is being painted is calculated by finding the area of each side and adding them together while excluding the back side. The cabinet has a height of 7 feet, a width of 4 feet, and a length of 2.5 feet. We calculate the surface area for each side as follows:
- Front (height × width): 7 ft × 4 ft = 28 square feet
- Sides (two sides, each height × length): 2 × (7 ft × 2.5 ft) = 35 square feet
- Top (width × length): 4 ft × 2.5 ft = 10 square feet
- Bottom (width × length): 4 ft × 2.5 ft = 10 square feet
Therefore, the surface area of the cabinet being painted is 83 square feet.
Now add the areas of these parts together:
28 sq ft + 35 sq ft + 10 sq ft + 10 sq ft = 83 square feet
Therefore, the surface area of the cabinet being painted is 83 square feet.