Question

a glass ornament will be designed using the net of the square pyramid shown in the diagram below. how many square centimeters of glass will be needed to manufacture the ornament if the base is made of plastic?

Explanation:

Step1: Calculate the area of one triangular face

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base \(b = 9\) cm and the height \(h=12\) cm.
\(A_{triangle}=\frac{1}{2}\times9\times12\)
\(A_{triangle}= 54\) \(cm^{2}\)

Step2: Find the total area of the four triangular faces

Since there are 4 congruent triangular faces in the square - pyramid net (and the base is made of plastic, so we don't consider it for the glass part).
\(A_{total}=4\times A_{triangle}\)
\(A_{total}=4\times54\)
\(A_{total}=216\) \(cm^{2}\)

Answer:

\(216\) square centimeters.