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Which of the following statements about the area of polygons is true?

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Question: Which of the following statements about the area of polygons is true?

Options:

  1. The area of a polygon can be calculated using the formula A = 1/2 * base * height.
  2. The area of a polygon is always greater than the area of its circumscribed circle.
  3. The area of a regular polygon can be calculated using the formula A = (1/4) * n * s^2 * cot(π/n).
  4. The area of a polygon is independent of its shape.

Correct Answer: The area of a regular polygon can be calculated using the formula A = (1/4) * n * s^2 * cot(π/n).

Solution: 

The area of a regular polygon can indeed be calculated using the formula A = (1/4) * n * s^2 * cot(π/n), where n is the number of sides and s is the side length.

Which of the following statements about the area of polygons is true?

Practice Questions

Q1
Which of the following statements about the area of polygons is true?
  1. The area of a polygon can be calculated using the formula A = 1/2 * base * height.
  2. The area of a polygon is always greater than the area of its circumscribed circle.
  3. The area of a regular polygon can be calculated using the formula A = (1/4) * n * s^2 * cot(π/n).
  4. The area of a polygon is independent of its shape.

Questions & Step-by-Step Solutions

Which of the following statements about the area of polygons is true?
  • Step 1: Understand what a polygon is. A polygon is a shape with straight sides, like a triangle or a square.
  • Step 2: Know what a regular polygon is. A regular polygon has all sides and angles equal, like a regular hexagon.
  • Step 3: Learn about area. The area is the amount of space inside a shape.
  • Step 4: Familiarize yourself with the formula for the area of a regular polygon: A = (1/4) * n * s^2 * cot(π/n).
  • Step 5: Identify the variables in the formula: 'n' is the number of sides, and 's' is the length of one side.
  • Step 6: Understand that this formula helps you calculate the area of any regular polygon if you know how many sides it has and the length of one side.
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