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 \(A = \frac{1}{2}bh\). For the base triangle with \(b = 6\space cm\) and \(h = 6\space cm\), we have \(A_{base}=\frac{1}{2}\times6\times6 = 18\space cm^{2}\)

Step2: Calculate the area of the three lateral triangles

• For the triangle with \(b = 6\space cm\) and \(h = 9\space cm\): \(A_1=\frac{1}{2}\times6\times9 = 27\space cm^{2}\)
• For the two triangles with \(b = 6\space cm\) and \(h = 3\space cm\): \(A_2 = 2\times(\frac{1}{2}\times6\times3)= 18\space cm^{2}\)

Step3: Sum up all the areas

The surface area \(S=A_{base}+A_1 + A_2\). Substitute the values: \(S=18 + 27+18=63\space cm^{2}\)

Answer:

\(63\space cm^{2}\)