Final answer:
The lateral area of a regular pentagonal pyramid with a slant height of 18 inches and a base side length of 9 inches is 405 square inches.
Step-by-step explanation:
To find the lateral area of a regular pentagonal pyramid, we need to find the area of each triangular face and then add them up. Since the base of the pyramid is a regular pentagon, each face will be an isosceles triangle. To find the lateral area, we need to calculate the area of one triangular face and then multiply it by 5 (the number of triangular faces).
The formula for the area of a triangle is 1/2 x base x height. In this case, the base of the triangle is the side length of the pentagon, which is 9 inches, and the height of the triangle is the slant height of the pyramid, which is 18 inches. Substituting these values into the formula, we get:
Area of one triangular face = 1/2 x 9 inches x 18 inches = 81 square inches
Since there are 5 triangular faces, the lateral area of the pyramid is:
Lateral area = 5 x 81 square inches = 405 square inches