Question

finding the surface area of an octahedron
this 8 - sided octahedron is a composite figure consisting of 2 square pyramids. the base of the pyramid is 33 mm, and the slant height is 28.6 mm.
what is the surface area of the octahedron?
mm²

Explanation:

Step1: Calculate the area of one triangular face

The formula for the area of a triangle is \(A = \frac{1}{2}bh\). Here, the base \(b = 33\) mm and the height (slant height) \(h=28.6\) mm.

$$A_{triangle}=\frac{1}{2}\times33\times28.6 = 471.9$$

Step2: Calculate the total number of triangular faces

Since the octahedron is made of 2 square - pyramids, and each square - pyramid has 4 triangular faces. So the total number of triangular faces \(n = 8\).

Step3: Calculate the surface area of the octahedron

Multiply the area of one triangular face by the number of triangular faces.

$$A = 471.9\times8=3775.2$$

Answer:

\(3775.2\)