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
58.25 in^2
47.25 in^2
52.25 in^2
To find the surface area of a triangular pyramid, you need to find the area of the base and the area of the three triangular faces.
The area of the base can be found using the formula for the area of a triangle, A = (1/2) * base * height. In this case, the base of the pyramid is 5 in. and the height is 4.3 in., so the area of the base is A = (1/2) * 5 in. * 4.3 in. = 10.75 in^2.
Next, to find the area of each triangular face, you can use the formula for the area of a triangle, A = (1/2) * base * height. You know the base of each triangular face is 5 in., and the slant height is 6 in. The height of the triangular face can be found using the Pythagorean theorem, where h^2 = slant height^2 - base^2, then h = √(6^2 - 5^2) = √(36 - 25) = √11.
Now you can calculate the area of each triangular face, A = (1/2) * base * height = (1/2) * 5 in. * √11 = 2.5√11 in^2.
Since the pyramid has three identical triangular faces, the total area of all the triangular faces is 3 * 2.5√11 = 7.5√11 in^2.
Finally, to find the total surface area of the pyramid, you need to add the area of the base and the area of the triangular faces. So the surface area is 10.75 in^2 + 7.5√11 in^2.
To get a numerical approximation, you can calculate the value of √11 and multiply it by 7.5, and then add 10.75.
Using a calculator, √11 ≈ 3.316625.
So the surface area is approximately 7.5 * 3.316625 in^2 + 10.75 in^2 = 24.872 in^2 + 10.75 in^2 ≈ 35.622 in^2.
Therefore, the correct answer is not listed among the given options.