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

Step2: Calculate the area of the three lateral triangles

• For the lateral triangle with base \(b = 9\space cm\) and height \(h = 3\space cm\), its area \(A_{1}=\frac{1}{2}\times9\times3=\frac{27}{2}=13.5\space cm^{2}\)
• The other two lateral triangles: one with base \(b = 6\space cm\) and height \(h = 6\space cm\) (area \(A_{2}=\frac{1}{2}\times6\times6 = 18\space cm^{2}\)), and another with base \(b = 6\space cm\) and height \(h = 6\space cm\) (area \(A_{3}=\frac{1}{2}\times6\times6 = 18\space cm^{2}\))

Step3: Sum up all the areas

The surface area \(S=A_{base}+A_{1}+A_{2}+A_{3}\)
\(S = 18+13.5 + 18+18\)
\(S=67.5\space cm^{2}\)

Answer:

\(67.5\space cm^{2}\)