Final answer:
To find the lateral area of a regular pentagonal pyramid with a slant height of 14 inches and a base edge of 6 inches, calculate the area of one triangular face and multiply by five. The area of one face is (6 in x 14 in) / 2, totaling 42 in². The lateral area is 5 x 42 in², equaling 210 in².
Step-by-step explanation:
The question asks us to find the lateral area of a regular pentagonal pyramid with a slant height of 14 inches and a base edge of 6 inches. To calculate the lateral area, we need to find the area of one of the triangular faces and then multiply that by the number of faces, which is five in the case of a pentagonal pyramid.
The area of one triangular face can be found using the formula for the area of a triangle, which is (base x height) / 2. In this case, the base of the triangle is the base edge of the pentagon (6 inches), and the height is the slant height of the pyramid (14 inches).
Area of one triangular face = (6 in x 14 in) / 2 = 42 in².
Since there are five triangular faces, the total lateral area is 5 x 42 in² which equals 210 in².