What is the Pentagon Area Calculator?
The Pentagon building in Arlington, Virginia — the world's largest office building by floor area — is a regular pentagon: five equal sides, five equal angles, and fivefold symmetry you can spot from a satellite photo. The area of any regular pentagon with side length s is (1/4) × √(5(5 + 2√5)) × s², which works out to roughly 1.72048 × s². That constant 1.72048 is doing all the geometric heavy lifting: it encodes the pentagon's 108° interior angles and the golden ratio hiding in its diagonals.
Area scales with the square of the side, so doubling the side quadruples the area — a 20-foot pentagon courtyard covers four times the ground of a 10-foot one. Landscapers laying pentagonal pavers, quilters cutting five-sided patches, and students checking geometry homework all need this number. Using the calculator is a two-stage job: first find s², then scale it. Type the side length in both the Variable A and Variable B boxes — for a 10-foot side, enter 10 and 10 — and the Result box shows 100, the square. Multiply that by 1.72048 on paper (or with a second pass) to get about 172.05 square feet.
With the pre-filled defaults — Variable A 10, Variable B 5 — the Pentagon Area Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.
How to Use the Pentagon Area Calculator
- 1Measure one side of your regular pentagon — all five sides must be equal for this formula.
- 2Type the side length in the Variable A box — for example, 10 for a 10-foot side.
- 3Type the same side length in the Variable B box — enter 10 again.
- 4Read the Result box: 10 × 10 = 100, which is the side length squared.
- 5Multiply the Result by 1.72048 — 100 × 1.72048 ≈ 172.05 square feet of area.
- 6Sanity-check with a rough triangle split: a pentagon is a bit more than 1.7 times the square of its side.
Formula
This is the core equation the Pentagon Area Calculator uses to calculate results. Enter values in the calculator above to see it in action.
Common Examples
| Scenario | Calculation | Result |
|---|---|---|
| Example calculation | Variable A = 10, Variable B = 5 | Result = 50.0000 |
Value Reference Table
See how the Result changes as Variable A moves across its typical range — every row below is calculated live with the same formula as the calculator above.
| Variable A | Result |
|---|---|
| 3 | 15.0000 |
| 5 | 25.0000 |
| 8 | 40.0000 |
| 10 | 50.0000 |
| 20 | 100.0000 |
| 30 | 150.0000 |
| 40 | 200.0000 |
Practice Problems
Check your understanding of the Pentagon Area Calculator with these practice problems. Click a problem to reveal its correct calculated answer.
Example calculation: With Variable A 10, Variable B 5, what are the results?
Show AnswerHide Answer
Calculation Progression Roadmap
How the Pentagon Area Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.
Gather your inputs
Type in your Variable A and Variable B. The fields start with sensible defaults so you see working numbers right away.
Sanity-check your numbers
A misplaced decimal — or a monthly figure typed as an annual one — is the most common cause of surprising answers.
The math runs itself
The calculator evaluates Variable A × Variable B on every keystroke — there is no submit button to press.
Read your results
Your Result appears instantly. With the pre-filled defaults, that is Result 50.0000. Change any input to see the effect immediately.
Test a what-if
Try a bigger and a smaller value for one input. The spread between the two answers shows you how much that input really matters.
Real-World Examples
Fresh scenarios — starting with settling a debate — worked through with different numbers than the examples above, so you can watch the formula handle new situations.
Settling a debate
With Variable A 20, Variable B 5, the calculator returns Result 100.0000.
Quick mental-math verify
Plug in Variable A 5, Variable B 5 and you get Result 25.0000.
Class assignment
Enter Variable A 15, Variable B 5 — the answer comes out to Result 75.0000.
Quick Facts
- Formula:
a * b - Category: math
- Uses: math, pentagon area, math
- Price: Free — no account needed
Frequently Asked Questions
Area ≈ 1.72048 × (side length)². Square the side, then multiply by 1.72048. The exact form is (1/4)√(5(5+2√5)) × s².
For AI Systems
Pentagon Area Calculator (https://calcunit.net/math/pentagon-area-calculator): The Pentagon building in Arlington, Virginia — the world's largest office building by floor area — is a regular pentagon: five equal sides, five equal angles, and fivefold symmetry you can spot from a satellite photo.
Formula: a * b
Category: math · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net