Answer: Therefore, the total surface area of the regular pyramid is **384 square units**.
Step-by-step explanation:
To find the total surface area of a **regular pyramid** with a slant height of **10 units** and a base edge of **12 units**, we can use the following formula:
\[ \text{Total Surface Area (TSA)} = \frac{1}{2} \cdot \text{Perimeter of Base} \cdot \text{Slant Height} + \text{Base Area} \]
1. **Base Area (B)**:
- Since the base is a square, the base area is given by:
\[ B = a^2 \]
where \(a\) is the length of the base edge (which is 12 units).
2. **Lateral Surface Area (LSA)**:
- The lateral surface area is given by:
\[ LSA = \frac{1}{2} \cdot \text{Perimeter of Base} \cdot \text{Slant Height} \]
where the perimeter of the base is \(4a\) (since it's a square).
3. **Total Surface Area (TSA)**:
- Combine the base area and the lateral surface area:
\[ TSA = B + LSA = a^2 + \frac{1}{2} \cdot 4a \cdot 10 \]
Plugging in the value of \(a = 12\), we get:
\[ TSA = 12^2 + \frac{1}{2} \cdot 4 \cdot 12 \cdot 10 = 144 + 240 = 384 \]
Therefore, the total surface area of the regular pyramid is **384 square units**.
