Question

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)

52.25 in.^2

47.25 in.^2

58.25 in.^2

55.75 in.^2

Answer 1

[AI-generated answer — Bot GPT 3.5]

The formula to find the surface area of a triangular pyramid is given by:

Surface Area = Base Area + (Triangle Area x Number of Triangle Faces)

First, let's find the base area of the pyramid. Since the base is a triangle, we can use the formula for the area of a triangle, which is:
Area = (1/2) x Base x Height

Substituting the given values, we have:
Base Area = (1/2) x 5 in. x 4.3 in.
Base Area = 10.75 in.^2

Next, let's find the area of each triangle face. Again, we can use the formula for the area of a triangle, which is:
Area = (1/2) x Base x Height

Substituting the given values, we have:
Triangle Area = (1/2) x 5 in. x 6 in.
Triangle Area = 15 in.^2

There are four triangle faces in a triangular pyramid, so the total area of the triangles is:
Triangle Area x Number of Triangle Faces = 15 in.^2 x 4 = 60 in.^2

Finally, we can find the surface area of the pyramid by adding the base area and the area of the triangle faces:
Surface Area = Base Area + (Triangle Area x Number of Triangle Faces)
Surface Area = 10.75 in.^2 + 60 in.^2
Surface Area = 70.75 in.^2

Therefore, the correct answer is 70.75 in.^2.