Question

use the net for the triangular pyramid to find the surface area.

Explanation:

Step1: Calculate the area of the base triangle

The formula for the area of a triangle is \(A = \frac{1}{2}\times base\times height\). For the base triangle with base \(b = 6\) cm and height \(h = 6\) cm, we have \(A_{base}=\frac{1}{2}\times6\times6= 18\) \(cm^{2}\).

Step2: Calculate the area of the three lateral triangles

Lateral triangle 1

With base \(b = 9\) cm and height \(h = 6\) cm, \(A_{1}=\frac{1}{2}\times9\times6 = 27\) \(cm^{2}\).

Lateral triangle 2

With base \(b = 6\) cm and height \(h = 6\) cm, \(A_{2}=\frac{1}{2}\times6\times6=18\) \(cm^{2}\).

Lateral triangle 3

With base \(b = 3\) cm and height \(h = 6\) cm, \(A_{3}=\frac{1}{2}\times3\times6 = 9\) \(cm^{2}\).

Step3: Calculate the total surface area

The total surface area \(A_{total}=A_{base}+A_{1}+A_{2}+A_{3}\). Substitute the values: \(A_{total}=18 + 27+18 + 9=72\) \(cm^{2}\).

Answer:

\(72\) \(cm^{2}\)