Isosceles Triangle Calculator
Calculate area, perimeter, height and angles of an isosceles triangle from its equal sides and base.
Inputs
units
units
Area
36.6606sq units
Perimeter
28.0000units
Height
9.1652units
Base Angle
66.4218°
Apex Angle
47.1564°
Step by step
Height from Pythagorean theorem
h = √(10² − (8/2)²)
= 9.1652
Area
A = ½ × 8 × 9.1652
= 36.6606
Perimeter
P = 2 × 10 + 8
= 28
How it works
An isosceles triangle has two equal sides (legs). The height is found using the Pythagorean theorem on the half-base and leg. Base angles are equal and found via inverse cosine.
Formulas
Height
h = √(leg² − (base/2)²)
- l
- Length of the equal side
- b
- Base length
Area
A = ½ × base × height
- b
- Base length
- h
- Height
Frequently Asked Questions
What if I only know the base angle and one side?
If you know the base angle θ and the leg, the base = 2 × leg × cos(θ). Enter those values to get all properties.
Can the apex angle be obtuse?
Yes. If base > leg × √2, the apex angle exceeds 90°.