Surface Area of Pyramids Quick Check
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Question
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
58.25 in.2
58.25 in. squared
52.25 in.2
52.25 in. squared
55.75 in.2
55.75 in. squared
47.25 in.2
To find the surface area of the chocolate pyramid, we need to calculate the areas of each of the triangular faces and the base.
The formula for the surface area of a triangular pyramid is:
Surface Area = base area + (0.5 × perimeter × slant height)
First, let's find the base area. The base is a triangle, so we can use the formula for the area of a triangle:
Base Area = 0.5 × base length × height of base
= 0.5 × 5 in × 4.3 in
= 10.75 in²
Next, let's calculate the perimeter of the base. Since the base is a triangle, we can find the perimeter by adding the lengths of all three sides:
Perimeter = 5 in + 5 in + 5 in
= 15 in
Now, we can calculate the surface area by plugging in the values into the formula:
Surface Area = 10.75 in² + (0.5 × 15 in × 6 in)
= 10.75 in² + (0.5 × 90 in²)
= 10.75 in² + 45 in²
= 55.75 in²
Therefore, the correct answer is 55.75 in.²