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)
• 55.75 in.?
• 58.25 in.?
47.25 in.?
52.25 in?
To find the surface area of the triangular pyramid, we need to calculate the areas of each of the four triangular faces and the area of the triangular base, then sum them up.
The formula to find the area of a triangle is 1/2 * base * height.
First, let's find the area of the triangular base:
Area of triangular base = 1/2 * base * height
= 1/2 * 5 in. * 4.3 in.
= 10.75 in^2
Next, let's find the areas of the triangular faces:
Area of a triangular face = 1/2 * base * height
= 1/2 * 5 in. * 6 in.
= 15 in^2
Now, let's sum up the areas of all the faces:
Surface area = 4 * area of triangular face + area of triangular base
= 4 * 15 in^2 + 10.75 in^2
= 60 in^2 + 10.75 in^2
= 70.75 in^2
So, the correct answer is 70.75 in^2.