Isosceles Triangle Perimeter Calculator

An isosceles triangle has two equal legs (s) and one different base (b).

P = b + 2s

A triangle with 6 cm base and 5 cm legs has perimeter 6 + 10 = 16 cm.

Validity check: for the triangle to close, the legs must each be longer than half the base (s > b/2). If s = b/2 exactly, the “triangle” collapses to a straight line of length b. If s < b/2, no triangle is possible.

Where isosceles triangles show up in real measurements:

• Party pennants and bunting. A standard bunting pennant is isosceles. A 6 in base × 8 in legs has perimeter 22 in. Twenty pennants need 440 in (~37 ft) of edge trim or rope.
• Pizza slices approximate isosceles triangles when the pizza is cut into equal slices. The legs are always the RADIUS, so a 16-inch pizza gives 8-in legs, not 16. Cut into 8 slices, each base measures 2 × 8 × sin(22.5°) = 6.12 in and the perimeter of one slice is 22.12 in.
• Roof rafters. Symmetric gable roofs are isosceles in cross-section: two equal rafter lengths plus the building width as the base.
• A-frame cabins and tents. The whole structure is one isosceles triangle repeated down its length, which is why every rafter in an A-frame is cut to the same length.
• Triangular flags. Most pennant flags are isosceles, and the two long edges are what gets hemmed.

Worked example: bunting for a backyard party

You’re making 25 pennants with 5-in bases and 7-in legs. Each pennant perimeter = 5 + 14 = 19 in. Total edge to hem = 25 × 19 = 475 in ≈ 40 ft of edge.

The string is a separate calculation, and it is the one people underestimate. The pennants themselves only occupy 25 × 5 = 125 in of it. Everything else is gaps and tie-offs: at a 3-in gap between pennants you add 72 in, plus a couple of feet at each end to reach the fixings. Call it 20 ft of string against 40 ft of hemming.

Worked example: a flagpole pennant

A nautical signal pennant with a 12 in base and 36 in legs (long, narrow shape). P = 12 + 72 = 84 in. Edge tape needed: 90 in (allowing for corner reinforcement).

Quick relations from base b and leg s:

• Perimeter: P = b + 2s
• Height (from apex perpendicular to base): h = √(s² − (b/2)²)
• Area: A = ½ × b × h = ½ × b × √(s² − b²/4)

Special case 1: when b = s, the triangle is equilateral. P = 3s. Special case 2: when b = s × √2, the apex angle is exactly 90° and you have an isosceles right triangle, the shape of half a square cut on the diagonal.

If you only know two angles (say the apex angle θ) and the base, the leg length is s = b / (2 × sin(θ/2)). Then plug into the perimeter formula.