Final answer:
The surface area of the octahedron is 288 square inches.
Step-by-step explanation:
An octahedron has six corners and eight sides. In order to find the surface area of the octahedron, we need to calculate the area of each individual triangle and then add them up. Each triangle is an equilateral triangle with a base of 12 inches and a height of half the base.
The formula for the area of a triangle is ½ × base × height. So, the area of each triangle is ½ × 12 inches × 6 inches = 36 square inches. Since there are 8 triangles, the total surface area of the octahedron is 8 × 36 square inches = 288 square inches.