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)

Answer 1

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.