https://file.aiquickdraw.com/mathbot/file/1726353310273us0ffgro.jpg

The image shows a net of a 3D rectangular prism (cuboid) made up of several rectangular faces. To calculate the surface area of this shape, we need to calculate the area of all its rectangular faces and then sum them up.

### Breakdown of the shape:
The net consists of 6 rectangles:
1. **Top and Bottom faces**: These are identical rectangles with dimensions 3 inches by 2 inches.
   - Area of each = \(3 \times 2 = 6\) square inches
   - Total for both = \(6 \times 2 = 12\) square inches

2. **Front and Back faces**: These are identical rectangles with dimensions 3 inches by 3 inches.
   - Area of each = \(3 \times 3 = 9\) square inches
   - Total for both = \(9 \times 2 = 18\) square inches

3. **Left and Right side faces**: These are identical rectangles with dimensions 2 inches by 3 inches.
   - Area of each = \(2 \times 3 = 6\) square inches
   - Total for both = \(6 \times 2 = 12\) square inches

### Total Surface Area:
\[
\text{Total Surface Area} = 12 + 18 + 12 = 42 \text{ square inches}
\]

Thus, the surface area of the rectangular prism is **42 square inches**.

Would you like more details or have any questions?

Here are 5 related questions to extend your understanding:
1. What is the surface area of a cube with a side length of 4 inches?
2. How do you calculate the surface area of a cylinder?
3. What is the difference between lateral surface area and total surface area?
4. How would the surface area change if one dimension of the prism was doubled?
5. Can the formula for surface area be applied to irregular shapes?

**Tip:** When calculating the surface area of a 3D object, always ensure that all faces are included in the total sum.

What is the surface area of the shape in the image, which is a rectangular prism?

Learn how to calculate the surface area of a rectangular prism with given dimensions: 3 inches by 2 inches by 3 inches. The solution covers key concepts in geometry and surface area calculation, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation