Question 1198259
**1. Find the Slant Height**

* We can use the Pythagorean theorem to find the slant height (the height of each triangular face of the pyramid).
* Imagine a right triangle formed by:
    * The base: Half the base edge of the octagon (12 inches / 2 = 6 inches)
    * The height: The slant height (which we'll call 's')
    * The hypotenuse: The lateral edge (18 inches)

* Using Pythagorean Theorem: 
    * s² = 18² - 6² 
    * s² = 324 - 36 
    * s² = 288 
    * s = √288 
    * s ≈ 16.97 inches

**2. Calculate the Area of One Triangular Face**

* Area of a triangle = (1/2) * base * height
* Area of one triangular face = (1/2) * base edge * slant height
* Area of one triangular face = (1/2) * 12 inches * 16.97 inches ≈ 101.82 square inches

**3. Calculate the Lateral Surface Area**

* The octagonal pyramid has 8 triangular faces.
* Lateral Surface Area = 8 * Area of one triangular face
* Lateral Surface Area = 8 * 101.82 square inches ≈ 814.58 square inches

**4. Round to the Nearest Integer**

* Lateral Surface Area ≈ 815 square inches

**Therefore, the lateral surface area of the regular octagonal pyramid is approximately 815 square inches.**