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Geometry

Isosceles Triangles

Isosceles triangle formulas. Free online Isosceles Triangles. Calculate isosceles triangles online — fast, accurate, mobile-friendly, no signup needed.

Two sides (and their opposite angles) are equal.
Height
4
Area
12

Derivation

  1. ├── 01Givena = 5, b = 6
  2. ├── 02FormulaHeight: √(t²-(a / 2)²)
  3. ├── 03Substitute√(t²-(5 / 2)²)
  4. ├── 04Compute Height4
  5. ├── 05FormulaArea: a / 2 × √(t²-(a / 2)²)
  6. ├── 06Substitute5 / 2 × √(t²-(5 / 2)²)
  7. └── 07Compute Area12
Did you know?

Pythagoras of Samos (c. 570–495 BCE) likely wasn’t the first to find a²+b²=c² — Babylonian tablets from ~1800 BCE used it — but the first rigorous proof is credited to his school.

§01What is

Understanding the Isosceles Triangles

The Isosceles Triangles computes Height from 2 inputs: equal sides, base. Isosceles triangle formulas.

Geometry is what turns raw measurements into useful answers about space — how much paint, how big a yard, how much material a project will need. Every craftsperson, architect, and DIYer reaches for these formulas regularly. The Isosceles Triangles sits in that toolkit — it isosceles triangle formulas. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

Height = √(t²-(a / 2)²) | Area = a / 2 × √(t²-(a / 2)²)

Where

a
Equal sides
b
Base
Height
Output value
Area
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Equal sides = 5, Base = 6.

  1. 01Start by noting the input — Equal sides: 5.
  2. 02Start by noting the input — Base: 6.
  3. 03Substitute these values into the formula: Height = √(t²-(a / 2)²) | Area = a / 2 × √(t²-(a / 2)²)
  4. 04Compute Height: the calculator returns 4.
  5. 05Compute Area: the calculator returns 12.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Isosceles Triangles Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Equal sides doubled

a = 10 (from 5)

Keep every other input at its default and double the equal sides. See how height responds.

  1. 01New Equal sides: 10
  2. 02Baseline Height: 4
  3. 03New Height: 9.53939
  4. 04Height increases by 138.5% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Base halved

b = 3 (from 6)

Keep every other input at its default and halve the base. See how height responds.

  1. 01New Base: 3
  2. 02Baseline Height: 4
  3. 03New Height: 4.7697
  4. 04Height increases by 19.2% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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