A pastry chef is creating a chocolate dessert in the shape of a triangle pyramid. The pyramid has a base of 5 inches. The height of the base is 4.3 inches in the slant height is 6 inches use the correct formula to find the surface area of the chocolate pyramid.
The surface area of a triangular pyramid can be found using the formula:
Surface Area = (Base Area) + (0.5 x Perimeter of the Base x Slant Height)
Given that the base of the pyramid is a triangle with a base of 5 inches and a height of 4.3 inches, we can calculate the area of the base as:
Base Area = (1/2) x base x height = (1/2) x 5 x 4.3 = 10.75 square inches
The slant height of the pyramid is given as 6 inches.
To find the perimeter of the base, we need to find the sum of the lengths of all three sides. Since only the base is given, we assume that the triangle is equilateral (all sides are equal). Therefore, each side has a length of 5 inches:
Perimeter of Base = 3 x base length = 3 x 5 = 15 inches
Now, we can calculate the surface area using the formula:
Surface Area = Base Area + (0.5 x Perimeter of the Base x Slant Height)
= 10.75 + (0.5 x 15 x 6)
= 10.75 + 45
= 55.75 square inches
Therefore, the surface area of the chocolate pyramid is 55.75 square inches.