Question: Workbook 2
Lesson 2.1: Surface Area of 3-D O
3. Determine the surface area of the square pyramid, to the nearest square inch.
50 inches
45 inches
Graph/figure: a square pyramid diagram is shown in the lower-left/center of the page, with the base labeled 45 inches and a slanted edge/lateral height labeled 50 inches.
1. **State the problem:** We need to find the surface area of a square pyramid with a base side length of $45$ inches and a slant height of $50$ inches.
2. **Formula for surface area of a square pyramid:**
$$\text{Surface Area} = \text{Base Area} + \text{Lateral Area}$$
where
$$\text{Base Area} = s^2$$
and
$$\text{Lateral Area} = 2 s l$$
Here, $s$ is the side length of the square base and $l$ is the slant height.
3. **Calculate the base area:**
$$\text{Base Area} = 45^2 = 2025 \text{ square inches}$$
4. **Calculate the lateral area:**
$$\text{Lateral Area} = 2 \times 45 \times 50 = 4500 \text{ square inches}$$
5. **Calculate total surface area:**
$$\text{Surface Area} = 2025 + 4500 = 6525 \text{ square inches}$$
6. **Round to the nearest square inch:** The surface area is already an integer, so
$$\boxed{6525 \text{ square inches}}$$
This is the total surface area of the square pyramid.