I need a correct answer A right triangular prism and its net are shown below.

Question

(All lengths are in millimeters.)

(a) Find the following side lengths for the net.

(b) Use the net to find the surface area of the prism.

Answer 1

To answer your question about the right triangular prism and its net, I need some specific values or dimensions from the diagram you're referring to. Unfortunately, I can't see the image you mentioned.

However, I can guide you on how to calculate the side lengths and surface area based on the dimensions provided for the triangular prism:

(a) Finding Side Lengths

For a right triangular prism, you generally have the following sides:

1. The base length of the triangle (which we can call $b$).
2. The height of the triangle (which we can call $h$).
3. The lengths of the two other sides of the triangle, depending on whether it is a right triangle or not.
4. The length of the prism itself (which we can call $L$).

Since I don't have the specific dimensions, please replace these variables with the measurements from your problem to find the lengths of the sides.

(b) Surface Area of the Prism

To find the surface area of a right triangular prism, you can use the formula:

$$\text{Surface Area}=\text{Area of the two triangular bases}+\text{Area of the three rectangular faces}$$

1. Area of the triangular base: If the base of the triangle is $b$ and the height is $h$, the area $A$ of one triangular base is: $$A=\frac{1}{2}\times b\times h$$ Since there are two triangular bases, you would multiply this by 2.

2. Area of the rectangular lateral faces: There are three rectangular faces. Their areas can be calculated as follows:

   • For the rectangle corresponding to the base $b$ of the triangle: $$A_1=b\times L$$
   • For the rectangle corresponding to the height $h$ of the triangle: $$A_2=h\times L$$
   • For the rectangle corresponding to the other side (let's call it $a$ for the hypotenuse or other side of the triangle): $$A_3=a\times L$$

3. Combine these areas: The total surface area $SA$ can be found by: $$SA=2\cdot A+A_1+A_2+A_3$$

Please provide the specific dimensions if you'd like help with calculations tailored to your problem.