To find the total area of the carpet Chad needs for the two rooms, we can calculate the area of each room separately and then sum those areas.
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{length} \times \text{width} \]
Room 1:
- Length = 12.5 feet
- Width = 10 feet
\[ \text{Area of Room 1} = 12.5 , \text{ft} \times 10 , \text{ft} = 125 , \text{square feet} \]
Room 2:
- Length = 15.75 feet (which is \( \frac{63}{4} \) feet or 15.75 feet)
- Width = 10 feet
\[ \text{Area of Room 2} = 15.75 , \text{ft} \times 10 , \text{ft} = 157.5 , \text{square feet} \]
Total Area:
\[ \text{Total Area} = \text{Area of Room 1} + \text{Area of Room 2} = 125 , \text{sq ft} + 157.5 , \text{sq ft} = 282.5 , \text{square feet} \]
Thus, the total area of the new carpet is \( \boxed{282.5} \) square feet.