Question

which expression can be used to find the surface area of the triangular prism? 1. $\frac{1}{2}cdot3cdot4 + 4cdot2+3cdot2 + 5cdot2$ 2. $(\frac{1}{2}cdot3cdot4)+4cdot2 + 3cdot2+5cdot2$ 3. $2cdot3cdot4+4cdot2 + 3cdot2+5cdot2$ 4. $4cdot2+3cdot2 + 5cdot2$

Explanation:

Step1: Recall surface - area formula for triangular prism

The surface area \(SA\) of a triangular prism is the sum of the areas of the two triangular bases and the three rectangular lateral faces. The area of a triangle is \(A_{triangle}=\frac{1}{2}bh\), and the area of a rectangle is \(A_{rectangle}=lw\).
For the triangular bases with base \(b = 3\) ft and height \(h = 4\) ft, the combined area of the two triangular bases is \(2\times\frac{1}{2}\times3\times4=3\times4\).
The three rectangular faces have dimensions: \(4\times2\), \(3\times2\), and \(5\times2\).

Step2: Write the surface - area expression

The surface - area expression of the triangular prism is \(2\times\frac{1}{2}\times3\times4 + 4\times2+3\times2 + 5\times2\).

Answer:

\(2\times\frac{1}{2}\times3\times4 + 4\times2+3\times2 + 5\times2\)