Isosceles Triangle Calculator
Calculate area, height, perimeter, and angles of an isosceles triangle from the base and equal side.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the Isosceles Triangle Calculator
Enter the base length and the equal side length. The calculator computes the area, height, perimeter, apex angle, and base angles.
- Enter the base. Type the length of the base (the unequal side).
- Enter the equal side. Type the length of one of the two equal sides.
- Read the results. The area is shown as the primary result. Height, perimeter, and angles appear in the breakdown below.
The height is calculated as sqrt(side^2 - (base/2)^2). The equal side must be longer than half the base to form a valid triangle.
About Isosceles Triangles
An isosceles triangle has two sides of equal length. The two angles opposite the equal sides (the base angles) are also equal. The height from the apex to the base bisects the base at a right angle. Isosceles triangles appear in architecture, bridge trusses, roof framing, and many engineering designs where symmetry is important.
Frequently Asked Questions
What is an isosceles triangle?
An isosceles triangle has two sides of equal length and two equal base angles. The third side (the base) can be any length, as long as the triangle inequality is satisfied.
How do you find the height of an isosceles triangle?
The height from the apex to the base is h = sqrt(s^2 - (b/2)^2), where s is the equal side length and b is the base length.
How do you find the angles of an isosceles triangle?
The apex angle is 2 * arcsin(base / (2 * side)). The two base angles are each (180 - apex angle) / 2.