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Draw a net for a rectangular prism with length (L), width (W), and height (H).

Mathematics

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Answer

This assessment task focuses on rectangular prisms. The first step is to draw a net for a rectangular prism.

Step-by-step solution

5 steps

A net is a two-dimensional pattern that can be folded to form a three-dimensional shape. For a rectangular prism, the net consists of six rectangles representing its faces.

Here's how to draw a net for a rectangular prism with length (LL), width (WW), and height (HH):

  1. Choose dimensions.

    Let's assume a rectangular prism with length L=5L = 5 cm, width W=3W = 3 cm, and height H=2H = 2 cm.

  2. Draw the central rectangle (base).

    Draw a rectangle representing the base of the prism. Its dimensions will be L×WL \times W.

    Base: 5 cm×3 cm\text{Base: } 5 \text{ cm} \times 3 \text{ cm}
  3. Draw the four side rectangles.

    Attach four rectangles to the sides of the central base rectangle. These will be the lateral faces.

    • Two rectangles will have dimensions L×HL \times H (e.g., 5 cm×2 cm5 \text{ cm} \times 2 \text{ cm}).
    • Two rectangles will have dimensions W×HW \times H (e.g., 3 cm×2 cm3 \text{ cm} \times 2 \text{ cm}). Arrange them alternatingly around the base. For example, attach a 5×25 \times 2 rectangle to one 5 cm5 \text{ cm} side, a 3×23 \times 2 rectangle to a 3 cm3 \text{ cm} side, another 5×25 \times 2 to the opposite 5 cm5 \text{ cm} side, and another 3×23 \times 2 to the remaining 3 cm3 \text{ cm} side.
  4. Draw the top rectangle.

    Attach one more rectangle to any of the L×HL \times H or W×HW \times H side faces. This will be the top face, and it must have the same dimensions as the base: L×WL \times W (e.g., 5 cm×3 cm5 \text{ cm} \times 3 \text{ cm}). A common way is to attach it to one of the L×HL \times H faces.

  5. Label the dimensions.

    Label all the sides of the rectangles with their corresponding lengths (LL, WW, or HH). For our example:

    • The base and top rectangles will have sides labeled 5 cm5 \text{ cm} and 3 cm3 \text{ cm}.
    • The two larger side rectangles will have sides labeled 5 cm5 \text{ cm} and 2 cm2 \text{ cm}.
    • The two smaller side rectangles will have sides labeled 3 cm3 \text{ cm} and 2 cm2 \text{ cm}.

    The net will look like a cross shape or a series of rectangles laid out flat, ready to be folded into a prism.

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