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 is 4.3 in., and the slant height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid. (1 point)
Responses
52.25 in.2
52.25 in. squared
55.75 in.2
55.75 in. squared
47.25 in.2
47.25 in. squared
58.25 in.2
To find the surface area of the chocolate pyramid, we need to find the areas of each of its faces and then add them together.
The formula for the area of a triangle is A = (1/2)bh, where A is the area, b is the base, and h is the height.
First, let's find the area of the base triangle:
Area of base triangle = (1/2)(5)(4.3) = 10.75 in²
Next, let's find the area of the four triangular faces (lateral faces):
Area of each triangular face = (1/2)(base)(height) = (1/2)(5)(6) = 15 in²
Since there are four triangular faces, the total area of the triangular faces is:
Total area of triangular faces = 4 * 15 = 60 in²
Lastly, let's find the area of the base square:
Area of base square = (base)(base) = 5 * 5 = 25 in²
Now, let's add up all the areas:
Total surface area = area of base triangle + total area of triangular faces + area of base square
= 10.75 + 60 + 25
= 95.75 in²
Therefore, the correct answer is 95.75 in².
one of the answers i gave you are correct
I apologize for the mistake. Let's calculate it again using the given measurements.
The formula for the surface area of a triangular pyramid is:
Surface Area = (base area) + 4 * (triangle area)
First, let's find the area of the base triangle:
Area of base triangle = (1/2) * base * height of base = (1/2) * 5 * 4.3 = 10.75 in²
Next, let's find the area of each triangular face:
Area of each triangular face = (1/2) * base * slant height = (1/2) * 5 * 6 = 15 in²
Now, let's calculate the total surface area:
Surface Area = 10.75 + 4 * 15 = 10.75 + 60 = 70.75 in²
Therefore, the correct answer is 70.75 in².