A pastry chef a 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 inches and the slant height is 6 inches use the correct formula to find the surface area of the chocolate pyramid
To find the surface area of the chocolate pyramid, we can use the formula for the surface area of a triangular pyramid:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
First, let's calculate the base area. Since the base is a triangle, we can use the formula for the area of a triangle:
Base Area = (1/2) * Base * Height
Base = 5 inches
Height = 4.3 inches
Base Area = (1/2) * 5 * 4.3
Base Area = 10.75 square inches
Next, let's calculate the perimeter of the base. Since the base is a triangle, we can use the formula for the perimeter of a triangle:
Perimeter of Base = Sum of the lengths of all three sides
To calculate the lengths of the sides, we can use the Pythagorean theorem. Since the base is a right triangle, one of the sides is the height and the other side is the base.
Side 1 = Base = 5 inches
Side 2 = Height = 4.3 inches
Using the Pythagorean theorem:
Side 3 = √(Side 1^2 + Side 2^2)
Side 3 = √(5^2 + 4.3^2)
Side 3 = √(25 + 18.49)
Side 3 = √43.49
Side 3 ≈ 6.59 inches
Perimeter of Base = Side 1 + Side 2 + Side 3
Perimeter of Base = 5 + 4.3 + 6.59
Perimeter of Base ≈ 15.89 inches
Now, let's calculate the surface area:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
Surface Area = 10.75 + (1/2) * 15.89 * 6
Surface Area = 10.75 + 7.945 * 6
Surface Area = 10.75 + 47.67
Surface Area ≈ 58.42 square inches
Therefore, the surface area of the chocolate pyramid is approximately 58.42 square inches.