Question

use the net for the triangular pyramid to find the surface area. 9 cm 6 cm 6 cm 6 cm 3 cm

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

Step2: Calculate the area of the three lateral triangles

There are two types of lateral triangles. One type has base \(b = 9\space cm\) and height \(h = 6\space cm\), and the other has base \(b = 6\space cm\) and height \(h = 3\space cm\).

• For the triangle with \(b = 9\space cm\) and \(h = 6\space cm\), \(A_{1}=\frac{1}{2}\times9\times6=27\space cm^{2}\)
• For the triangle with \(b = 6\space cm\) and \(h = 3\space cm\), \(A_{2}=\frac{1}{2}\times6\times3 = 9\space cm^{2}\)

Since there are two triangles of the second - type, the total area of the lateral triangles is \(A_{lateral}=27 + 2\times9=27 + 18=45\space cm^{2}\)

Step3: Calculate the total surface area

The surface area \(S\) of the triangular pyramid is the sum of the area of the base and the lateral areas. So \(S=A_{base}+A_{lateral}=27 + 45=99\space cm^{2}\)

Answer:

\(99\space cm^{2}\)