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
55.75 in.2
55.75 in. squared
58.25 in.2
58.25 in. squared
47.25 in.2
47.25 in. squared
52.25 in.2
To find the surface area of the chocolate pyramid, we need to find the area of each triangular face and the base.
The formula for the area of a triangle is A = 1/2 * base * height.
The area of each triangular face can be calculated as follows:
A = 1/2 * 5 in * 4.3 in
A = 10.75 in²
Since the chocolate pyramid has 4 triangular faces, the total area of the triangular faces is:
10.75 in² * 4 = 43 in²
The formula for the area of a rectangle (the base) is A = length * width.
For the base, the length is 5 in and the width is 5 in.
A = 5 in * 5 in
A = 25 in²
Now, to find the total surface area, we add the area of the triangular faces to the base area:
43 in² + 25 in² = 68 in²
Therefore, the correct answer is 68 in².
aint a answer
Apologies for the incorrect response. Let's calculate the correct answer.
To find the surface area of the triangular pyramid, we need to find the areas of the four triangular faces and the base.
The formula for the area of a triangle is A = 1/2 * base * height.
Using the given measurements:
Area of each triangular face = 1/2 * 5 in * 6 in = 15 in²
Since the pyramid has four triangular faces, the total area of the triangular faces is:
15 in² * 4 = 60 in²
To find the area of the base, we use the formula for the area of a rectangle:
Area of the base = length * width = 5 in * 5 in = 25 in²
Finally, to find the total surface area, we add the area of the triangular faces and the base:
Total surface area = 60 in² + 25 in² = 85 in²
Therefore, the correct answer is 85 in².
still aint a answer choice
Apologies for the confusion. Let's reconsider the answer choices and calculate the correct surface area of the chocolate pyramid.
The formula for the surface area of a triangular pyramid is given by:
Surface Area = base area + 1/2 * perimeter of base * slant height
First, let's calculate the base area:
Base Area = 1/2 * base * height of base = 1/2 * 5 in * 4.3 in = 10.75 in²
Next, let's calculate the perimeter of the base:
Perimeter of Base = sum of lengths of all sides of the base triangle
= 5 in + 5 in + 5 in = 15 in
Now, let's substitute the values into the surface area formula:
Surface Area = 10.75 in² + 1/2 * 15 in * 6 in
= 10.75 in² + 1/2 * 90 in²
= 10.75 in² + 45 in²
= 55.75 in²
Therefore, the correct answer is 55.75 in.²