Which of the following expressions represent the surface area, in square inches, of the triangular prism created by this net? Select three that apply.
Understand the Problem
The question provides a description of a 2D net of a triangular prism. It asks to select the correct expressions that can be used to calculate the surface area of the triangular prism. The solution will involve determining the area of each face (rectangles and triangles) and summing them up. We need to consider that there are three rectangular faces and two triangular faces that make up the surface area of the prism.
Answer
$(l_1 \times w_1 + l_2 \times w_2 + l_3 \times w_3) + (b \times h)$
Answer for screen readers
The surface area of the triangular prism is the sum of the areas of its faces. The expressions that can be used to calculate the surface area are of the form:
$(l_1 \times w_1 + l_2 \times w_2 + l_3 \times w_3) + (b \times h)$
Steps to Solve
- Identify the faces of the triangular prism
A triangular prism has 5 faces: 3 rectangles and 2 triangles.
- Calculate the area of one of the rectangular faces
The area of a rectangle is length times width. Let's denote the length of the rectangle as $l$ and the width as $w$. Area of one rectangle = $l \times w$
- Calculate the total area of the three rectangular faces
Since we potentially have different dimensions, we must consider them separately Area of the three rectangles = $l_1 \times w_1 + l_2 \times w_2 + l_3 \times w_3$
- Calculate the area of one triangular face
The area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$. Let's denote the base as $b$ and the height as $h$. Area of one triangle = $\frac{1}{2} \times b \times h$
- Calculate the total area of the two triangular faces
Since a prism has two identical triangles, we multiply the area of one triangle by 2. Area of two triangles $= 2 \times (\frac{1}{2} \times b \times h) = b \times h$
- Calculate the total surface area of the triangular prism
Add the total area of the three rectangles and the total area of the two triangles. Total Surface Area $= (l_1 \times w_1 + l_2 \times w_2 + l_3 \times w_3) + (b \times h)$
The surface area of the triangular prism is the sum of the areas of its faces. The expressions that can be used to calculate the surface area are of the form:
$(l_1 \times w_1 + l_2 \times w_2 + l_3 \times w_3) + (b \times h)$
More Information
The formula represents the sum of areas of the three rectangular faces and the two triangular faces of the prism.
Tips
A common mistake is to forget to multiply the area of one triangle by 2, since there are two triangular faces. Also, if the rectangles do not have the same dimensions, one must take care to denote them differently and sum each area separately instead of cubing one area.
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