A pastry chef is creating a chocolate dessert in the shape of a triangular pyramid the pyramid has a base of 5 in and the height of the base is 4.3 in and the slant height of 6 in use the correct formula to find surface area of the chocolate pyramid
To find the surface area of a triangular pyramid, we need to find the area of the base and the areas of the triangular faces.
1. Area of the Base:
Since the base is a triangle, we can use the formula for the area of a triangle:
Area = (base length * height) / 2.
Substituting the given values, we have:
Area of the base = (5 in * 4.3 in) / 2 = 21.5 in².
2. Areas of the Triangular Faces:
To find the area of each triangular face, we can use the formula for the area of a triangle with the side lengths and slant height.
However, we need to start by finding the length of the sides of the triangle.
Using the Pythagorean theorem, we can find the side lengths of the triangle.
a² + b² = c², where c is the slant height and a and b are the two sides of the triangle:
4.3² + b² = 6²,
18.49 + b² = 36,
b² = 36 - 18.49,
b² = 17.51,
b = √17.51 = 4.18 in (approximately).
Now we can calculate the area of each triangular face:
Area of each triangular face = (base length * height) / 2 = (5 in * 4.18 in) / 2 = 10.45 in².
3. Total Surface Area:
Since the pyramid has 4 triangular faces, we need to multiply the area of one triangular face by 4 to get the total surface area:
Total surface area = 4 * (10.45 in²) = 41.8 in².
Therefore, the surface area of the chocolate pyramid is 41.8 square inches.