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.
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
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