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 correctr formula to find the surface area of the chocolate pyramid.

Answer 1

To find the surface area of the chocolate pyramid, we need to find the area of each face and then add them together.

The formula for the surface area of a triangular pyramid is:
Surface Area = base area + (0.5 x perimeter of base x slant height)

First, let's find the base area. Since the base is a triangular pyramid, its base area can be calculated using the formula for the area of a triangle:
Base Area = (1/2) x base x height of base
Base Area = (1/2) x 5 in. x 4.3 in.
Base Area = 10.75 in²

Now, let's find the perimeter of the base. Since the base is a triangle, we can find the perimeter by adding the lengths of all three sides:
Perimeter of Base = 5 in. + 5 in. + 5 in.
Perimeter of Base = 15 in.

Now, substituting the values into the formula for the surface area of a triangular pyramid:
Surface Area = 10.75 in² + (0.5 x 15 in. x 6 in.)
Surface Area = 10.75 in² + (0.5 x 90 in²)
Surface Area = 10.75 in² + 45 in²
Surface Area = 55.75 in²

Therefore, the surface area of the chocolate pyramid is 55.75 square inches.