Last updated: July 31, 2026
Isosceles Triangle Side Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
b = (P - a)/2, h = √(b² - (a/2)²), Area = (a×h)/2
Where:
- P=Perimeter
- a=Base
- b=Equal leg
- h=Height
- A=Area
Worked Examples
Perimeter 20 with base 6
A standard valid isosceles triangle.
- 1Compute the equal leg: b = (20 - 6)/2 = 7.
- 2Find the height: h = √(7² - 3²) = √40 ≈ 6.324555.
- 3Compute area: A = (6 × 6.324555)/2 ≈ 18.973666.
Perimeter 30 with base 10
A symmetric triangle with easy arithmetic.
- 1b = (30 - 10)/2 = 10.
- 2h = √(10² - 5²) = √75 ≈ 8.660254.
- 3Area = (10 × 8.660254)/2 ≈ 43.301270.
Invalid perimeter and base
A base that is too large breaks triangle validity.
- 1b = (10 - 8)/2 = 1.
- 2Check 2b > a → 2 > 8 fails.
- 3The inputs do not form a valid isosceles triangle.
Introduction
Use this calculator when you know the perimeter and base of an isosceles triangle and want the equal side length, height, and area in one step. It applies the perimeter relation first, then checks whether the resulting sides really form a valid triangle.
Formula Overview
The equal leg comes directly from the perimeter once the base is known.
Perimeter relation: P = a + 2b.
Solve for the leg: b = (P - a)/2.
Height comes from splitting the base into two equal halves.
Area follows from A = (base × height)/2.
What to Enter
Only two measurements are needed for this version of the calculator.
Enter the full perimeter P.
Enter the base a, the unequal side.
Use consistent units for both inputs.
Decimals are allowed for measured dimensions.
Triangle Validity Rules
Not every perimeter-base pair creates a real triangle.
Both values must be positive.
Perimeter must be greater than the base.
The derived leg must remain positive.
The triangle inequality reduces to 2b > a for this setup.
Worked Example
The sample P = 20 and a = 6 shows the full workflow.
b = (20 - 6)/2 = 7.
h = √(49 - 9) = √40 ≈ 6.324555.
A = (6 × 6.324555)/2 ≈ 18.973666.
All values are reported to 6 decimal places.
How to Read the Output
The calculator returns both the derived leg and secondary geometric properties.
Leg is the length of each equal side.
Height is the perpendicular distance from the apex to the base.
Area uses the echoed base and computed height.
Echoed base and perimeter make manual checking easier.
Common Uses
This calculator is helpful anywhere symmetric triangular panels or frames appear.
Roof truss sketches and framing layouts.
Craft, signage, and fabric cutting plans.
Geometry homework involving isosceles triangles.
Quick verification of measured perimeter/base pairs.
FAQs
What if the perimeter equals the base?
Then the equal legs become zero, so no triangle exists.
Why is 2b > a required?
An isosceles triangle still has to satisfy triangle inequality, and with equal legs that condition becomes 2b > a.
Can I use decimals?
Yes. The calculator accepts decimal inputs and returns rounded decimal outputs.
Why is height computed from a right triangle?
Dropping the altitude bisects the base and creates two congruent right triangles.
Does the calculator return the area too?
Yes. It returns leg, base, perimeter, height, and area.
What units are used?
The calculator is unit-free. If you enter inches, the outputs are in inches and square inches conceptually.