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)
Responses
55.75 in.2
55.75 in. squared
47.25 in.2
47.25 in. squared
58.25 in.2
58.25 in. squared
52.25 in.2
To find the surface area of a triangular pyramid, we use the formula:
Surface Area = Base Area + Lateral Area
The base area of the pyramid can be found using the formula for the area of a triangle:
Base Area = (1/2) * base * height
Substituting the given values, we get:
Base Area = (1/2) * 5 in. * 4.3 in.
Base Area = 10.75 in.²
The lateral area of the pyramid can be found using the formula:
Lateral Area = (1/2) * perimeter * slant height
The perimeter of the triangular base can be found by adding the lengths of all three sides:
Perimeter = 5 in. + 5 in. + 6 in.
Perimeter = 16 in.
Substituting the values into the formula, we get:
Lateral Area = (1/2) * 16 in. * 6 in.
Lateral Area = 48 in.²
Now, we can find the total surface area:
Surface Area = Base Area + Lateral Area
Surface Area = 10.75 in.² + 48 in.²
Surface Area = 58.75 in.²
Therefore, the correct answer is: 58.75 in.²