Isosceles Triangle Calculator
This isosceles triangle calculator returns height, area, perimeter and both kinds of angle. Example: with base 6 and legs of 5 the height is 4 and the area 12.
Example: Known values: Base and leg · Base a 6 · Leg b 5 → Result: Base a = 6 · leg b = 5 · height h = 4 · area A = 12. Source: Wikipedia – Isosceles triangle. Updated: .
How it is calculated
An isosceles triangle has two equal sides, the legs, and two equal base angles. The height to the base bisects the base and the apex angle and splits the triangle into two right triangles.
Formulas and steps
With base a and leg b: h = √(b² − (a/2)²), A = a · h / 2 and P = a + 2b. The base angle is α = arccos(a / (2b)) and the apex angle γ = 180° − 2α. If you know base and height, b = √(h² + (a/2)²). From leg b and apex angle γ you get a = 2b · sin(γ/2) and h = b · cos(γ/2).
Worked example
Base a = 6, leg b = 5: half the base is 3, so h = √(25 − 9) = 4. The area is 6 · 4 / 2 = 12 and the perimeter 6 + 10 = 16. The base angle is arccos(0.6) ≈ 53.1301°, the apex angle 180° − 2 · 53.1301° ≈ 73.7398°. With leg 5 and γ = 90°, by contrast, a ≈ 7.07107, h ≈ 3.53553 and A = 12.5.
- If the base equals the leg the triangle is equilateral, with three angles of 60°.
- At γ = 90° the triangle is both right-angled and isosceles; each base angle is 45°.
Frequently asked questions
How do you find the height of an isosceles triangle?
With Pythagoras: h = √(b² − (a/2)²). For base 6 and leg 5, h = √(25 − 9) = 4.
What are the angles of an isosceles triangle?
The two base angles are equal: α = arccos(a / (2b)). The apex angle is 180° − 2α; in the example 53.1301° and 73.7398°.
How do I calculate the area?
A = base · height / 2. For base 6 and height 4 that gives 12 square units.
Sources and legal basis
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