A chocolate dessert is in the shape of a square pyramid. The pyramid is represented with a net. How many square inches of icing are needed for the faces of the dessert? 5in 3in 3in 3in 3in (1 point)
The total surface area of the square pyramid can be calculated by adding the area of the base (which is a square) and the area of the four triangular faces.
Area of the base (square):
Each side of the square base is 3 inches, so the area is 3in x 3in = 9in².
Area of each triangular face:
The base of the triangle is 3 inches and the height can be calculated using the Pythagorean theorem: h² = 3² + (3/2)² = 9 + 2.25 = 11.25
h = √11.25 ≈ 3.35 inches
Using the formula for the area of a triangle (0.5 * base * height):
Area of each triangular face = 0.5 x 3 x 3.35 ≈ 5.025in²
There are 4 triangular faces, so the total area of the triangular faces is 4 x 5.025in² = 20.1in².
Adding the area of the base and the triangular faces:
Total surface area = 9in² + 20.1in² = 29.1in²
So, approximately 29.1 square inches of icing are needed for the faces of the dessert.