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 4.3in and the slant height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid.
52.25
47.25
55.75
58.25
To find the surface area of the triangular pyramid, we need to find the area of each individual face and then sum them up.
The formula for the surface area of a triangular pyramid is:
Surface Area = Area of Base + Area of Each Triangle Face
First, let's find the area of the base. The base is in the shape of a triangle, and to find its area, we use the formula:
Area of Triangle = (base * height) / 2
In this case, the base of the triangle is 5in and the height is 4.3in.
Area of Base = (5 * 4.3) / 2 = 21.5in²
The next step is to find the area of each triangular face. Each face is an isosceles triangle, and to find its area, we can use the formula:
Area of Isosceles Triangle = (base * height) / 2
In this case, the base of each triangular face is 5in (same as the base of the pyramid's base) and the height is the slant height, which is 6in.
Area of Each Triangle Face = (5 * 6) / 2 = 15in²
Now, we can find the total surface area by summing up the area of the base and the area of each triangular face.
Surface Area = Area of Base + Area of Each Triangle Face
Surface Area = 21.5in² + (15in² * 4)
Surface Area = 21.5in² + 60in²
Surface Area = 81.5in²
Therefore, the correct answer is 81.5, which is not among the given options.