Inradius of Heptagon given Area Calculator

Inradius Formula:

\[ r_i = \frac{\sqrt{\frac{4A \tan(\pi/7)}{7}}}{2 \tan(\pi/7)} \]

Inradius of Heptagon (m):

1. What is Inradius of a Heptagon?

Definition: The inradius of a heptagon is the radius of the circle inscribed inside the heptagon that touches all seven sides.

Purpose: Knowing the inradius is important for geometric calculations, construction planning, and design of heptagonal shapes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_i = \frac{\sqrt{\frac{4A \tan(\pi/7)}{7}}}{2 \tan(\pi/7)} \]

Where:

\( r_i \) — Inradius of the heptagon (meters)
\( A \) — Area of the heptagon (square meters)
\( \pi \) — Mathematical constant pi (~3.14159)
\( \tan \) — Tangent trigonometric function

Explanation: The formula calculates the radius of the inscribed circle based on the area of the regular heptagon.

3. Importance of Inradius Calculation

Details: The inradius helps determine the maximum circle that fits inside a regular heptagon, useful in engineering and design applications.

4. Using the Calculator

Tips:

Enter the area of the heptagon in square meters
Specify tolerance percentage (±5% range)
Area must be > 0
Tolerance must be between -5% and +5%

5. Frequently Asked Questions (FAQ)

Q1: What is a regular heptagon?
A: A regular heptagon is a seven-sided polygon with all sides equal and all angles equal.

Q2: Why include a tolerance factor?
A: The tolerance allows for practical adjustments accounting for material variations or construction tolerances.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect regular heptagon.

Q4: Can I use this for irregular heptagons?
A: No, this calculator only works for regular heptagons where all sides and angles are equal.

Q5: What's the relationship between inradius and side length?
A: For a regular heptagon with side length 's', the inradius can also be calculated as \( r_i = \frac{s}{2 \tan(\pi/7)} \).