Tip: This is the most direct mode. Enter the two distinct adjacent sides.
We’ll compute b = r·a and then P = 2(a + b).
We will split d₁ into y₁ and y₂ in proportion k.
Note: Diagonals alone aren’t enough—you must specify how d₁ is split into y₁ and y₂ (or give their ratio).
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Enter vertices in order around the shape (clockwise or counter‑clockwise). We’ll verify the kite condition (two equal adjacent side pairs) within a small tolerance.
Supported rows:
sides,a,b or diagonals,d1,d2,y1,y2. Units use the selector above.| # | Mode | Inputs | a | b | P | s | Area* | Status |
|---|
*Area shown only when computable (e.g., diagonals known).
Live Diagram
Labels: a, b, d₁, d₂Diagram is illustrative. Proportions adjust based on your input mode.
Results
Perimeter
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Semiperimeter s
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Side a
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Side b
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Area (when available)
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Area A = (d₁·d₂)/2 when both diagonals are known.
Step‑by‑Step
Choose a mode and enter values to see the working...
Notes: For diagonal‑split mode you must specify y₁ + y₂ = d₁ (or provide their ratio).
Coordinates mode requires a valid kite (two equal adjacent sides).
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Kite Perimeter & Geometry Guide
Everything you need to understand the formulas, symbols, and workflows—plus visual diagrams.
1) Geometry Basics
A kite has two pairs of equal adjacent sides and perpendicular diagonals. One diagonal (the axis) bisects the other. The perimeter depends on the two distinct adjacent side lengths a and b.
2) Symbols & Definitions
| Symbol | Meaning |
|---|---|
| a, b | Distinct adjacent side lengths of the kite. |
| d₁ | Axis diagonal that bisects the other diagonal. |
| d₂ | Bisected diagonal (perpendicular to d₁). |
| y₁, y₂ | Segments of d₁ split by d₂ (y₁ + y₂ = d₁). |
| x | Half of d₂ (x = d₂ / 2). |
| P, s | Perimeter P and semiperimeter s = P/2. |
3) Perimeter Formulas at a Glance
| Case | Formula | Notes |
|---|---|---|
| General | P = 2(a + b) | Always valid for kites. |
| Rhombus (a = b) | P = 4a | Special case of a kite. |
| Diagonal‑split | a = √(x² + y₁²), b = √(x² + y₂²), P = 2(a + b) | x = d₂/2; y₁ + y₂ = d₁. |
4) Why Diagonals Alone Don’t Fix P
Knowing just d₁ and d₂ is insufficient because many kites can share the same diagonals but have different splits (y₁, y₂) of d₁, leading to different a and b, hence different P.
5) Deriving the Diagonal‑Split Formula
- Let x = d₂/2. The diagonals are perpendicular, so each side forms a right triangle with legs x and y₁ (or y₂).
- By Pythagoras: a = √(x² + y₁²) and b = √(x² + y₂²).
- Perimeter is the sum of the four sides: two a’s and two b’s → P = 2(a + b).
6) Input Modes — Quick Reference
| Mode | Required Inputs | Formula Path | Typical Use |
|---|---|---|---|
| Sides | a, b | P = 2(a + b) | Direct measurements available. |
| Ratio | a, r = b/a | b = r·a → P = 2(a + b) | Proportional designs and scaling. |
| Diagonal‑split | d₁, d₂, and y₁ & y₂ or ratio k | x = d₂/2; a,b via √(x² + y²); P = 2(a + b) | When diagonals are easiest to measure. |
| Coordinates | Four vertices (x, y) ordered around shape | Distance between consecutive vertices; detect equal adjacent pairs | CAD exports and survey points. |
7) Worked Example
Given: d₁ = 18 cm split as y₁ = 7 cm, y₂ = 11 cm; d₂ = 12 cm → x = 6 cm.
a = √(6² + 7²) = √(36 + 49) = √85 ≈ 9.220 cm; b = √(6² + 11²) = √(36 + 121) = √157 ≈ 12.530 cm.
P = 2(a + b) ≈ 2(9.220 + 12.530) = 43.500 cm; s = 21.750 cm.
8) Pitfalls & Tips
- Keep units consistent; the calculator propagates the chosen unit.
- For diagonal‑split, ensure y₁ + y₂ = d₁ (or provide a clean ratio p:q).
- Coordinates must trace the boundary in order—no crossing or reordering.
- Nearly equal a and b suggests a rhombus—use the P = 4a shortcut.