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 height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid

Answer 1

The surface area formula for a triangular pyramid is:
Surface Area = (1/2) x base x height + (1/2) x side1 x slant height1 + (1/2) x side2 x slant height2 + (1/2) x side3 x slant height3

In this case, the base of the pyramid is a triangle with a base of 5 in and a height of 4.3 in. So the base area is (1/2) x 5 in x 4.3 in = 10.75 in^2.

To find the slant height of the triangular pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle, with the height of the base (4.3 in) as one leg and the height of the pyramid (6 in) as the other leg. So, we have:

slant height = √(4.3^2 + 6^2)
slant height ≈ √(18.49 + 36)
slant height ≈ √54.49
slant height ≈ 7.38 in

Now, let's calculate the surface area of the pyramid:
Surface Area = (1/2) x base x height + (1/2) x side1 x slant height1 + (1/2) x side2 x slant height2 + (1/2) x side3 x slant height3

Surface Area = 10.75 in^2 + (1/2) x 5 in x 7.38 in + (1/2) x 5 in x 7.38 in + (1/2) x 5 in x 7.38 in

Surface Area ≈ 10.75 in^2 + 18.425 in^2 + 18.425 in^2 + 18.425 in^2
Surface Area ≈ 65.025 in^2

Therefore, the surface area of the chocolate pyramid is approximately 65.025 square inches.