How many planes are shown in the figure?
Understand the Problem
The question is asking how many planes are represented in the provided geometric figure. To answer this, we need to analyze the figure and identify the distinct planes visible.
Answer
$6$
Answer for screen readers
There are $6$ planes shown in the figure.
Steps to Solve
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Identify the geometric figures in the image
The figure shows a rectangular prism (box) positioned above a green plane. -
Determine the visible planes
A plane is a flat surface that extends infinitely. In the figure, we can identify:- The green plane (bottom)
- The top face of the rectangular prism (the face formed by points K, L, M, P)
- The four vertical faces of the prism (each pair of opposite faces)
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Count the distinct planes
Each face of the prism counts as a separate plane alongside the green base. The total number of planes includes:- 1 green plane (bottom)
- 1 top face of the prism
- 2 vertical faces on one side
- 2 vertical faces on the opposite side
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Calculate the total
Thus, we have:- 1 green plane
- 1 top plane
- 4 vertical planes
Summing these gives us a total of:
$$ 1 + 1 + 4 = 6 $$
There are $6$ planes shown in the figure.
More Information
In a three-dimensional figure, every flat face represents a distinct plane, and horizontal or vertical faces contribute to the count. It's vital to identify all such faces properly.
Tips
- Counting the same plane multiple times, especially when visualizing complex shapes.
- Overlooking any vertical faces which might not be immediately visible in the figure.
