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A rectangular pyramid is labeled with the following dimensions. The front left edge of the rectangular base is labeled 6. The front right edge of the rectangular base is labeled 4. There is a dashed line labeled 4 that extends from the apex to the middle of the line labeled 6. There is another dashed line labeled 4 point 6 that extends from the apex to the middle of the line labeled 4.

The rectangular pyramid could be decomposed into which of the following nets?

(1 point)
Responses

A rectangle has 4 triangles connected to it.
Image with alt text: A rectangle has 4 triangles connected to it.

A rectangle has 4 triangles connected to it.
Image with alt text: A rectangle has 4 triangles connected to it.

A rectangle has 4 triangles connected to it.
Image with alt text: A rectangle has 4 triangles connected to it.

A rectangle has 4 triangles connected to it.
Image with alt text: A rectangle has 4 triangles connected to it.
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1 answer

To determine which net accurately represents the rectangular pyramid described, we need to analyze the dimensions of the pyramid.

  1. A rectangular pyramid has a rectangular base and four triangular faces that connect the apex to the corners of the base.

  2. The base dimensions from the description are:

    • One side of the rectangle (6 units) is longer.
    • The other side of the rectangle (4 units) is shorter.

  3. The dashed lines represent the heights of the triangular faces from the apex to the midpoints of the base edges. The triangular faces will have:

    • Two triangles with a base of 6 units each (one on each side of the longer base edge).
    • Two triangles with a base of 4 units each (one on each side of the shorter base edge).

Given the information, when the pyramid is decomposed into a net, it will consist of one rectangle (the base) with four triangles (the triangular faces) connected to it.

Based on this structure, the correct net of the rectangular pyramid would indeed be a rectangle with 4 triangles connected to it.

Thus, the answer is:

A rectangle has 4 triangles connected to it.