Question

an octahedron and its net are shown below. all the faces are the same size and shape. what is the surface area of the octahedron? 576 cm² 998.4 cm² 1,152 cm² 499.2 cm²

Explanation:

Step1: Find area of one triangular face

The formula for the area of a triangle is $A = \frac{1}{2} \times base \times height$. Here, base = 12 cm and height = 10.4 cm. So, area of one face is $\frac{1}{2} \times 12 \times 10.4 = 6 \times 10.4 = 62.4$ $cm^2$.

Step2: Count number of faces

An octahedron has 8 triangular faces (since all faces are same size and shape, and from the net we can see the structure with 8 triangles).

Step3: Calculate total surface area

Multiply area of one face by number of faces: $62.4 \times 8 = 499.2$ $cm^2$.

Answer:

499.2 $cm^2$