Question

which expression can be used to find the surface area of the triangular prism? 2(\frac{1}{2}\cdot3\cdot4)+4\cdot2 + 3\cdot2+5\cdot2
what is the surface area of the triangular prism?
s.a. = ft²

Explanation:

Step1: Calculate area of triangular faces

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 3$ ft and $h=4$ ft. There are 2 triangular faces, so the combined area of the triangular faces is $2\times(\frac{1}{2}\times3\times4)$.

Step2: Calculate area of rectangular faces

There are three rectangular faces with dimensions: one with dimensions $4\times2$, one with dimensions $3\times2$ and one with dimensions $5\times2$. Their areas are $4\times2$, $3\times2$ and $5\times2$ respectively. The sum of the areas of the rectangular faces is $4\times2 + 3\times2+5\times2$.

Step3: Calculate total surface - area

The surface - area (S.A.) of the triangular prism is the sum of the areas of the triangular faces and the rectangular faces.
\[

$$\begin{align*} S.A.&=2\times(\frac{1}{2}\times3\times4)+4\times2 + 3\times2+5\times2\\ &=2\times6+(8 + 6+10)\\ &=12 + 24\\ &=36 \end{align*}$$

\]

Answer:

36