Question

the figure shows a net of a triangular prism. which expression can be used to find the surface area of the prism? (3 4)+(3 3)+(3 5)+2(\frac{1}{2} 3 * 4) what is the surface area of the prism? s.a. = in.²

Explanation:

Step1: Analyze the net components

A triangular - prism net has 2 triangular faces and 3 rectangular faces. The area of a triangle is $A_{triangle}=\frac{1}{2}bh$ and the area of a rectangle is $A_{rectangle}=lw$. The bases of the triangular prism are right - triangles with base $b = 4$ in and height $h = 3$ in, and the rectangles have dimensions: $3\times4$, $3\times3$, and $3\times5$.

Step2: Calculate the area of triangular faces

The area of one triangular face is $\frac{1}{2}\times3\times4$. Since there are 2 triangular faces, their combined area is $2\times(\frac{1}{2}\times3\times4)$.

Step3: Calculate the area of rectangular faces

The areas of the three rectangular faces are $3\times4$, $3\times3$, and $3\times5$ respectively.

Step4: Calculate the total surface area

The surface area $S.A.$ of the triangular prism is the sum of the areas of the triangular and rectangular faces, so $S.A.=(3\times4)+(3\times3)+(3\times5)+2\times(\frac{1}{2}\times3\times4)$.
Now, calculate the value:
\[

$$\begin{align*} S.A.&=(3\times4)+(3\times3)+(3\times5)+2\times(\frac{1}{2}\times3\times4)\\ &=12 + 9+15+12\\ &=48 \end{align*}$$

\]

Answer:

48