Solved examples: Surface area of rectangular prisms using nets

📚 Quick Study Guide

• 📐 What is a Net? A net is a 2D pattern that can be folded to form a 3D shape. For a rectangular prism, the net consists of six rectangles.
• 📏 Surface Area Formula: The surface area (SA) of a rectangular prism is the sum of the areas of all its faces. If $l$ is the length, $w$ is the width, and $h$ is the height, then: $SA = 2lw + 2lh + 2wh$
• ✍️ Using Nets: To find the surface area using a net, calculate the area of each rectangle in the net and then add all those areas together.
• ➕ Units: Make sure all measurements are in the same units before calculating the area. The final answer will be in square units (e.g., $cm^2$, $m^2$, $in^2$).
• 💡 Tip: Label each rectangle in the net with its dimensions to avoid confusion during calculation.

Practice Quiz

1. A rectangular prism net has the following dimensions: two rectangles are 5cm x 3cm, two are 4cm x 3cm, and two are 5cm x 4cm. What is the surface area of the prism?

   1. 15 $cm^2$
   2. 47 $cm^2$
   3. 94 $cm^2$
   4. 100 $cm^2$

2. Which of the following is NOT a correct unit for surface area?

   1. $m^2$
   2. $cm^2$
   3. $ft^3$
   4. $in^2$

3. A net of a rectangular prism has dimensions: length=8cm, width=4cm, and height=2cm. What is the surface area of the rectangular prism?

   1. 32 $cm^2$
   2. 64 $cm^2$
   3. 96 $cm^2$
   4. 112 $cm^2$

4. What is the area of one face of a cube with side length 6cm?

   1. 6 $cm^2$
   2. 12 $cm^2$
   3. 24 $cm^2$
   4. 36 $cm^2$

5. A rectangular prism has a length of 10cm, a width of 5cm, and a height of 3cm. What is its surface area?

   1. 150 $cm^2$
   2. 190 $cm^2$
   3. 220 $cm^2$
   4. 230 $cm^2$

6. Consider a rectangular prism whose net consists of six identical squares, each with a side of 4cm. What is the surface area?

   1. 16 $cm^2$
   2. 64 $cm^2$
   3. 96 $cm^2$
   4. 128 $cm^2$

7. The net of a rectangular prism shows the following faces: two faces each with an area of 20 $cm^2$, two faces each with an area of 15 $cm^2$, and two faces each with an area of 12 $cm^2$. What is the total surface area of the prism?

   1. 35 $cm^2$
   2. 47 $cm^2$
   3. 94 $cm^2$
   4. 100 $cm^2$