Isosceles Triangle Area Calculator
Find the area of an isosceles triangle instantly — supply the two equal sides and the base, or enter the base and height directly.
Known inputs
Area = ½ × base × height
- 1
Height (Pythagorean theorem)
√(5² − (6 ÷ 2)²) = √(16) = 4 - 2
Area
½ × 6 × 4 = 12
How does this calculator work?
The area of an isosceles triangle with equal sides a and base b is ½ × b × √(a² − (b/2)²). Equivalently, supply the base and height directly: Area = ½ × b × h. Both require 2a > b. The calculator also reports the perimeter, angles, and the equal side inferred from base and height.
Formula
How this is calculated
The area of any triangle is ½ × base × height, where the height is the perpendicular distance from the apex to the base. For an isosceles triangle with two equal sides of length a and base b, the apex lies symmetrically above the midpoint of the base, so the height can be derived from the Pythagorean theorem: h = √(a² − (b/2)²). The area then follows as A = ½ × b × √(a² − (b/2)²).
If you already know the height (for example from a drawing or measurement), you can bypass the side calculation and enter the base and height directly. The calculator then computes the equal side as a = √(h² + (b/2)²) and reports all remaining properties.
The formula requires that 2a > b (the triangle inequality) — if the two equal sides together do not exceed the base, the triangle cannot close and no area exists. Similarly, if a ≤ b/2 then h would be imaginary, which means the legs are too short to reach the apex above the base.
Frequently asked questions
Area = (b / 4) × √(4a² − b²), which simplifies to ½ × b × h where h = √(a² − (b/2)²). Both forms are equivalent; the calculator uses the height form internally.
Use "Equal side and base" if you know the lengths of the two equal sides and the base (common in textbook problems). Use "Base and height" if you know the perpendicular height directly, for example from a ruler measurement.
No. Area is a property of the shape, not its orientation. Whether the triangle stands upright on its base or is tilted, the enclosed area is the same as long as the side lengths do not change.
TG we-Calculate Editorial Team. (2026). Isosceles Triangle Area Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/isosceles-triangle-area-calculator
TG we-Calculate Editorial Team. "Isosceles Triangle Area Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/isosceles-triangle-area-calculator.
TG we-Calculate Editorial Team, "Isosceles Triangle Area Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/isosceles-triangle-area-calculator
@misc{wecalculate_isosceles_triangle_area_calculator, title = {Isosceles Triangle Area Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/isosceles-triangle-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
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