The garden sculpture is a square pyramid with dimensions provided in the net diagram. To find the surface area of the garden sculpture, including the base, we need to calculate the area of the square base and the four triangular faces. The base is a square with each side measuring 10 feet. The area of the square is: Area of square = side × side = 10 ft × 10 ft = 100 ft² Each of the four triangles has a base of 10 feet (the same as the side of the square) and a height of 12 feet. The area of each triangle is: Area of triangle = (base × height) / 2 = (10 ft × 12 ft) / 2 = 60 ft² Since there are four triangles, the total area of the triangular faces is: Total area of triangles = 4 × 60 ft² = 240 ft² To find the total surface area of the sculpture, we add the area of the square base to the combined area of the triangular faces: Total surface area = area of square + total area of triangles = 100 ft² + 240 ft² = 340 ft² Therefore, the surface area of the garden sculpture, including the base, is 340 square feet (ft²).

To calculate the surface area of a square pyramid, which includes the base and the four triangular faces, we use the given dimensions from the net diagram.

First, we find the area of the base: Since the base is a square with a side of 10 feet, we can calculate the area by: Area of square base = side × side Area of square base = 10 ft × 10 ft Area of square base = 100 ft²

Next, we calculate the area of one of the triangular faces: Each triangular face has a base of 10 feet and a height of 12 feet. The area of a triangle is given by: Area of triangle = (base × height) / 2 Area of one triangle = (10 ft × 12 ft) / 2 Area of one triangle = 120 ft² / 2 Area of one triangle = 60 ft²

We then multiply this area by the number of triangular faces (which is 4): Total area of the four triangles = 60 ft² × 4 Total area of the four triangles = 240 ft²

Finally, we sum the areas of the base and the triangular faces to get the total surface area: Total surface area = area of the base + total area of the triangles Total surface area = 100 ft² + 240 ft² Total surface area = 340 ft²

Thus, the total surface area of the garden sculpture, including the base, is 340 square feet.

Extra: When we talk about surface area in geometry, we refer to the sum of the areas of all faces and surfaces on a three-dimensional shape. For pyramids, specifically square pyramids like the garden sculpture in the question, we have a square base and triangular side faces.

In general, to find the surface area of any geometric shape, you need to: 1. Calculate the area of every distinct face of the shape. 2. Add up these areas.

For a square pyramid, the process involves calculating the area of the square base using the formula for the area of a square (side × side) and then calculating the area of each of the triangular faces using the formula for the area of a triangle ((base × height) / 2). The base of each triangular face is the same as a side of the square base, and the height is the perpendicular distance from the base to the apex of the pyramid (not the slant height).

Understanding surface area is useful in various real-life applications, such as determining the amount of material needed to cover a shape (like fabric, paint, or in this case, possibly metal or stone for a sculpture). It is a concept that is frequently taught in mathematics, especially in the study of geometry.