The Correct Answer and Explanation is:
The correct answer is 384 cm².
To find the surface area of the square pyramid, we must calculate the total area of all its faces. The provided net is very helpful because it lays the three-dimensional shape flat, showing us that the pyramid is composed of one square base and four identical triangular faces. The calculation is a two part process: finding the area of the base and finding the area of the four sides.
First, we calculate the area of the square base. The formula for the area of a square is side multiplied by side. The diagram shows that the side length of the square base is 12 cm. Therefore, the area of the base is 12 cm × 12 cm, which equals 144 cm². This single calculation gives us the area for the bottom face of the pyramid.
Second, we calculate the area of the four triangular faces. These four triangles make up the lateral area of the pyramid. The formula for the area of a triangle is 0.5 × base × height. From the diagram, we can see that the base of each triangle corresponds to a side of the square, so its length is 12 cm. The height of each triangle is the pyramid’s slant height, which is given as 10 cm. Using these values, the area of one triangular face is 0.5 × 12 cm × 10 cm = 60 cm².
Since the pyramid has four of these identical triangular faces, we multiply the area of one triangle by four to find their total combined area. This calculation is 4 × 60 cm², which equals 240 cm².
Finally, to determine the total surface area of the pyramid, we add the area of the square base and the total area of the four triangular faces together. The final step is 144 cm² + 240 cm² = 384 cm².
