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
To find the surface area of the chocolate pyramid, you will need to calculate the areas of the base and the triangular faces.
The formula to find the surface area of a triangular pyramid is:
Surface_Area = (Area_Base) + (Area_Triangle1) + (Area_Triangle2) + (Area_Triangle3)
Step 1: Calculate the area of the base.
Area_Base = (1/2) * Base * Height
Area_Base = (1/2) * 5 * 4.3
Step 2: Calculate the area of each triangular face.
To find the area of a triangular face, you will need to use Heron's formula.
S = (Side1 + Side2 + Side3) / 2
Area_Triangle = √(S * (S - Side1) * (S - Side2) * (S - Side3)), where S = (Side1 + Side2 + Side3) / 2
For Triangle 1:
Side1 = Slant Height
Side2 = Base
Side3 = Height
S = (6 + 5 + 4.3) / 2
Area_Triangle1 = √(S * (S - 6) * (S - 5) * (S - 4.3))
For Triangle 2:
Side1 = Slant Height
Side2 = Base
Side3 = Height
S = (6 + 5 + 4.3) / 2
Area_Triangle2 = √(S * (S - 6) * (S - 5) * (S - 4.3))
For Triangle 3:
Side1 = Slant Height
Side2 = Base
Side3 = Height
S = (6 + 5 + 4.3) / 2
Area_Triangle3 = √(S * (S - 6) * (S - 5) * (S - 4.3))
Step 3: Add up all the areas.
Surface_Area = (Area_Base) + (Area_Triangle1) + (Area_Triangle2) + (Area_Triangle3)
To find the surface area of a triangular pyramid, you need to find the area of the base and the area of the triangular faces.
The formula for the area of a triangular pyramid is:
Surface Area = Area of Base + Area of Triangular Faces
The area of the base of a triangular pyramid is found by multiplying the base length and the height of the base and dividing by 2.
Area of Base = (length of base * height of base) / 2
Plugging in the values given:
Area of Base = (5 * 4.3) / 2 = 21.5 square inches
Now, let's find the area of the triangular faces. Since the slant height is given, we can use the formula for the area of a triangle:
Area of a Triangle = (base length * height) / 2
Plugging in the values given:
Area of Triangular Faces = (5 * 6) / 2 = 15 square inches
Now, we can find the surface area by adding the area of the base and the area of the triangular faces:
Surface Area = Area of Base + Area of Triangular Faces
Surface Area = 21.5 + 15 = 36.5 square inches
Therefore, the surface area of the chocolate pyramid is 36.5 square inches.