How many sides does a heptagon have ? (a) 2 (b) 4 (c) 7 (d) 5
The Correct Answer and Explanation is:
Correct Answer: (c) 7
A heptagon is a geometric figure that falls under the category of polygons. A polygon is a closed two-dimensional shape made up of straight line segments. The prefix “hepta” comes from the Greek word for seven, and the suffix “-gon” comes from the Greek word “gonia,” which means angle. Therefore, a heptagon is a seven-sided polygon with seven angles.
Each side of a heptagon connects to another at a vertex, forming a total of seven vertices. If the heptagon is regular, all of its sides and angles are equal. The sum of the interior angles of any polygon can be calculated using the formula:
(n − 2) × 180 degrees,
where n is the number of sides.
For a heptagon:
(n − 2) × 180 = (7 − 2) × 180 = 5 × 180 = 900 degrees.
So, the sum of the interior angles of a heptagon is 900 degrees.
Each interior angle of a regular heptagon is 900 ÷ 7, which is approximately 128.57 degrees.
Understanding the number of sides in polygons is fundamental in geometry. For example:
- A triangle has 3 sides
- A quadrilateral has 4 sides
- A pentagon has 5 sides
- A hexagon has 6 sides
- A heptagon has 7 sides
- An octagon has 8 sides
This naming pattern helps identify and distinguish between different shapes quickly. Recognizing a heptagon as having 7 sides is essential for tasks in mathematics, design, engineering, and architecture where polygonal shapes are used. Therefore, the correct answer to the question is clearly (c) 7.Correct Answer: (c) 7
A heptagon is a geometric figure that falls under the category of polygons. A polygon is a closed two-dimensional shape made up of straight line segments. The prefix “hepta” comes from the Greek word for seven, and the suffix “-gon” comes from the Greek word “gonia,” which means angle. Therefore, a heptagon is a seven-sided polygon with seven angles.
Each side of a heptagon connects to another at a vertex, forming a total of seven vertices. If the heptagon is regular, all of its sides and angles are equal. The sum of the interior angles of any polygon can be calculated using the formula:
(n − 2) × 180 degrees,
where n is the number of sides.
For a heptagon:
(n − 2) × 180 = (7 − 2) × 180 = 5 × 180 = 900 degrees.
So, the sum of the interior angles of a heptagon is 900 degrees.
Each interior angle of a regular heptagon is 900 ÷ 7, which is approximately 128.57 degrees.
Understanding the number of sides in polygons is fundamental in geometry. For example:
- A triangle has 3 sides
- A quadrilateral has 4 sides
- A pentagon has 5 sides
- A hexagon has 6 sides
- A heptagon has 7 sides
- An octagon has 8 sides
This naming pattern helps identify and distinguish between different shapes quickly. Recognizing a heptagon as having 7 sides is essential for tasks in mathematics, design, engineering, and architecture where polygonal shapes are used. Therefore, the correct answer to the question is clearly (c) 7.
