A pastry chef is creating a chocolate dessert in the shape of a triangular pyramid. The pyramid has a base of 5 in., the height of the base is 4.3 in., and the slant height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid. (1 point)

Question

Responses

58.25 in.2
58.25 in. squared

52.25 in.2
52.25 in. squared

47.25 in.2
47.25 in. squared

55.75 in.2

Answer 1

To find the surface area of the triangular pyramid, we can use the formula:

Surface Area = Base Area + (0.5 × Perimeter × Slant Height)

First, let's find the base area of the pyramid. The base is a triangle with a base length of 5 in. and a height of 4.3 in. The formula for the area of a triangle is:

Base Area = 0.5 × base length × height
= 0.5 × 5 in. × 4.3 in.
= 10.75 in.²

Now, let's find the perimeter of the base. The base is a triangle with sides of length 5 in. each. So, the perimeter is:

Perimeter = 3 × side length
= 3 × 5 in.
= 15 in.

Now, we can substitute the values into the formula:

Surface Area = 10.75 in.² + (0.5 × 15 in. × 6 in.)
= 10.75 in.² + 45 in.²
= 55.75 in.²

Therefore, the correct surface area of the chocolate pyramid is 55.75 in.².