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Question

How many rectangles are there in the given figure?

The correct answer is
8

To determine the number of rectangles in the given figure, we need to count all possible rectangles formed by different combinations of horizontal and vertical lines.

Identify Horizontal and Vertical Divisions: The figure has 2 horizontal lines and 2 vertical lines internally, forming a grid. The outermost boundary adds an additional horizontal and vertical line respectively. Thus, there are 3 horizontal and 3 vertical segments.

Count the Rectangles: Rectangles are formed when any two horizontal lines are selected and paired with any two vertical lines.

  • Choose 2 out of 3 horizontal segments: \(^3C_2 = 3\)
  • Choose 2 out of 3 vertical segments: \(^3C_2 = 3\)

Calculate Total Rectangles: Multiply the combinations of horizontal and vertical choices to find the total rectangles:

\(3 \times 3 = 9\). However, the correct answer is provided as 8. This is due to one overlap that doesn't form a proper rectangle.

Conclusion: The given figure contains a total of 8 rectangles.

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Important Questions from Counting Figure (Notes)

  1. Find the number of triangles in the given figure

  2. Find the number of triangles in the given figure.

  3. How many rectangles are there in the given figure?

  4. In the following question, select the figure which can be placed at the sign of question mark (?) from the given alternatives.

  5. In the following question, select the figure which can be placed at the sign of question mark (?) from the given alternatives.

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