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
55.75 in.2
55.75 in. squared
47.25 in.2
47.25 in. squared
52.25 in.2
To find the surface area of a triangular pyramid, you can use the formula:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
First, let's find the base area of the pyramid. Since the base is in the shape of a triangle, you can use the formula for the area of a triangle:
Base Area = (1/2) * Base * Height of Base
= (1/2) * 5 in. * 4.3 in.
= 10.75 in²
Next, let's find the perimeter of the base of the pyramid. Since the base has 3 sides, the perimeter is 3 times the length of one side. In this case, since it's a triangle with a base of 5 in., each side has a length of 5 in.
Perimeter of Base = 3 * Base
= 3 * 5 in.
= 15 in.
Now, let's substitute the values into the formula for the surface area:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
= 10.75 in² + (0.5 * 15 in. * 6 in.)
= 10.75 in² + 45 in.²
= 55.75 in²
Therefore, the correct answer is 55.75 in.².