Question: Work out the surface area of this pyramid.
13 cm
6 cm
Graph/shape: a pyramid is shown in the center of the page; the front base edge is labeled 6 cm near the bottom-left/center, and a slanted face height marked with a right-angle symbol is labeled 13 cm near the lower center.
1. **State the problem:** Calculate the surface area of a pyramid with a square base edge of $6$ cm and a slant height of $13$ cm.
2. **Formula for surface area of a pyramid:**
$$\text{Surface Area} = \text{Base Area} + \text{Lateral Area}$$
where
- Base Area for a square base = $s^2$
- Lateral Area = $\frac{1}{2} \times \text{Perimeter of base} \times \text{Slant height}$
3. **Calculate the base area:**
$$\text{Base Area} = 6^2 = 36 \text{ cm}^2$$
4. **Calculate the perimeter of the base:**
$$\text{Perimeter} = 4 \times 6 = 24 \text{ cm}$$
5. **Calculate the lateral area:**
$$\text{Lateral Area} = \frac{1}{2} \times 24 \times 13 = 12 \times 13 = 156 \text{ cm}^2$$
6. **Calculate total surface area:**
$$\text{Surface Area} = 36 + 156 = 192 \text{ cm}^2$$
**Final answer:** The surface area of the pyramid is $192$ cm$^2$.