Question

The surface area of a triangular pyramid is 305 square inches. The area of the base is 35 square inches. Each face has a base of 9. What is the slant height? 

DON'T ANSWER THE QUESTION! I ALREADY HAVE THE ANSWER. SORRY, I JUST GOT THE ANSWER. I DON'T KNOW HOW TO DELETE THIS QUESTION.

Answer 1

To find the slant height of a triangular pyramid, we can use the formula for the surface area of the pyramid and the area of the base. By substituting the given values into the formula, we can solve for the slant height which is 67.78 inches

Step-by-step explanation:

To find the slant height of a triangular pyramid, we need to use the formula for the surface area of the pyramid and the area of the base. The formula for the surface area of a triangular pyramid is given by:

Surface Area = (1/2) × Perimeter of Base × Slant Height

Given that the surface area is 305 square inches and the area of the base is 35 square inches, we can substitute these values into the formula and solve for the slant height:

305 = (1/2) × 9 × Slant Height

Simplifying the equation:

305 = 4.5 × Slant Height

Slant Height = 305 / 4.5

Slant Height ≈ 67.78 inches

Answer 2

Subtract 35 from 305, and you get 270. The formula for the area of a triangle, where b is base and h is height, is b * h / 2. There are three faces, or 3 triangles, and we know the base, so we can say that 3 * 9 * h / 2 = 270 => 27 * h / 2 = 270 => 27 * h / 2 * 2 = 270 * 2 => 27 * h = 540 => 27 * h / 27 = 540 / 27 => h = 20, so the slant height is 20 inches.