Question

a triangular pyramid is shown below. which diagram is a net for this pyramid? what is the surface area of the triangular pyramid? square centimeters

Explanation:

Step1: Calculate the area of the base

The base is a triangle with base \(b = 12\) cm and height \(h=10.4\) cm.
The area of a triangle is \(A=\frac{1}{2}\times b\times h\).
So, \(A_{base}=\frac{1}{2}\times12\times10.4 = 6\times10.4=62.4\) \(cm^{2}\)

Step2: Calculate the area of the three congruent triangular faces

Each triangular face has base \(b = 12\) cm and height \(h = 16\) cm.
The area of a triangle is \(A=\frac{1}{2}\times b\times h\).
For one face: \(A_{face}=\frac{1}{2}\times12\times16=6\times16 = 96\) \(cm^{2}\)
For three faces: \(A_{three - faces}=3\times96=288\) \(cm^{2}\)

Step3: Calculate the total surface area

The total surface area \(A_{total}=A_{base}+A_{three - faces}\)
\(A_{total}=62.4 + 288=350.4\) \(cm^{2}\)

Answer:

\(350.4\)