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.
A. 52.25 in.^2
B. 55.75 in.^2
C. 58.25 in.^2
D. 47.25 in.^2
To find the surface area of the triangular pyramid, we need to find the area of each triangular face and the base.
The area of each triangular face can be found using the formula A = (1/2) * base * height.
For the base, it is a triangle with a base of 5 in and a height of 4.3 in. Thus, the area of the base is (1/2) * 5 * 4.3 = 10.75 in^2.
The area of each triangular face can be found using the formula A = (1/2) * base * height. The base of each triangular face is 5 in and the height of each triangular face can be found using the Pythagorean theorem. The height is the square root of (slant height^2 - base^2), which, in this case, is the square root of (6^2 - 5^2) = √11.
Therefore, the area of each triangular face is (1/2) * 5 * √11 = 5/2 * √11 in^2.
So, the total surface area is the sum of the area of the base and the area of each triangular face. Thus, the surface area is 10.75 in^2 + 5/2 * √11 in^2.
Approximating the square root of 11 to two decimal places is 3.32, and simplifying the expression, we have 10.75 + 5/2 * 3.32 in^2 = 10.75 + 41.5 in^2 = 52.25 in^2.
Therefore, the correct answer is A. 52.25 in.^2.