Geometry
Polygon Area Calculator
Specify the side length and number of sides to get a regular polygon’s area, perimeter, apothem, circumradius, and interior/exterior angles.
Enter the number of sides and a side length to get area, perimeter, apothem, and interior/exterior angles.
Regular polygon formulas
Perimeter = n·s Apothem = s / [2·tan(π/n)] Area = ½ · Perimeter · Apothem
n is the number of sides (≥3) and s is the side length. Interior angle = (n − 2)·180° / n while the exterior angle is 360° / n.
How to use
- Enter how many equal sides the polygon has (triangle = 3, hexagon = 6, etc.).
- Provide the side length using any unit.
- Review area, perimeter, apothem, circumradius, and the interior/exterior angles.
Example
Input: n = 8, side length = 5 cm
Output: Area ≈ 120.7 cm², Perimeter = 40 cm, Apothem ≈ 4.14 cm, Interior angle = 135°
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Polygon Area Calculator: Polygon Area Calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic. Each resource is interlinked so crawlers (and readers) can discover the next best action within a couple of clicks—one of the easiest ways to lift topical authority.
Deep dive & study plan
The Polygon Area Calculator is a go-to tool whenever you need to area, perimeter, apothem, and angles for any regular polygon.. It focuses on regular polygon, area, perimeter, which means searchers often arrive with intent-heavy queries like “how to polygon area calculator quickly” or “polygon area calculator formula explained.” Use this calculator to capture those intents and keep learners on the page long enough to send positive engagement signals.
Under the hood, the calculator leans on n is the number of sides (≥3) and s is the side length. interior angle = (n − 2)·180° / n while the exterior angle is 360° / n.—that’s why we surface the full expression (“Perimeter = n·s Apothem = s / [2·tan(π/n)] Area = ½ · Perimeter · Apothem”) directly above the interactive widget. When you embed that formula inside H2s or supporting paragraphs, you help both humans and crawlers understand what entity the page represents.
Execution matters as much as the math. Follow the built-in procedure: Step 1: Enter how many equal sides the polygon has (triangle = 3, hexagon = 6, etc.). Step 2: Provide the side length using any unit. Step 3: Review area, perimeter, apothem, circumradius, and the interior/exterior angles.. Each numbered instruction is short enough to scan on mobile but descriptive enough to satisfy Google’s Helpful Content guidelines. Encourage students to jot down units, double-check signs, and compare answers with the Example card to build confidence.
The Example section itself is packed with semantic clues: “n = 8, side length = 5 cm” leading to “Area ≈ 120.7 cm², Perimeter = 40 cm, Apothem ≈ 4.14 cm, Interior angle = 135°.” Pepper similar narratives throughout your copy (and internal links from related guides) so canonical search intents are answered without pogo-sticking back to Google.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Link out to at least two related calculators to keep readers exploring your topical hub.
FAQ & notes
Does this work for irregular polygons?
No. The formulas assume every side and angle is identical. For irregular polygons use coordinate-based area methods instead.
Can I enter radius instead of side length?
This tool expects side length. Convert radius to side length first using s = 2r · sin(π/n) if needed.
What formula does the Polygon Area Calculator use?
n is the number of sides (≥3) and s is the side length. Interior angle = (n − 2)·180° / n while the exterior angle is 360° / n.
How do I use the Polygon Area Calculator?
Enter how many equal sides the polygon has (triangle = 3, hexagon = 6, etc.). Provide the side length using any unit. Review area, perimeter, apothem, circumradius, and the interior/exterior angles.