Types of Triangles
7 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
Triangles are the simplest closed shape and the building blocks of geometry. Every triangle can be described in two ways: by the lengths of its sides and by the size of its angles. Knowing the types helps you choose the right formula and spot shortcuts.
Classified by sides
| Type | Sides | Angles |
|---|---|---|
| Equilateral | All three equal | All 60° |
| Isosceles | Two equal | The angles opposite the equal sides are equal |
| Scalene | All different | All different |
Classified by angles
- Acute: all angles less than 90°.
- Right: one angle exactly 90°. The longest side (the hypotenuse) is opposite it.
- Obtuse: one angle greater than 90°.
Rules every triangle obeys
The three angles always add up to 180°. The sum of any two sides must be greater than the third (the triangle inequality), so sides 3, 4 and 8 cannot form a triangle because 3 + 4 < 8. The largest angle is opposite the longest side.
Perimeter and area
Perimeter is the sum of the sides. Area = ½ × base × height. For a right triangle with legs 5 and 12 (hypotenuse 13), the area is ½ × 5 × 12 = 30 and the perimeter is 30. For an equilateral triangle with side 6, the height is 3√3 ≈ 5.196, so the area is ½ × 6 × 5.196 ≈ 15.59, which is (√3/4) × 36 = 9√3. When you know only the sides, use Heron’s formula. Solve any triangle with the triangle calculator.
Special right triangles
The 45-45-90 triangle has sides in the ratio 1 : 1 : √2. The 30-60-90 triangle has sides in the ratio 1 : √3 : 2. See the Pythagorean theorem guide for triples such as 3-4-5.
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- Solve a triangle with sides 5, 12 and 13.
Show answer
Side a: 5 · Side b: 12 · Side c: 13
- A right triangle has legs 9 and 12. Find the hypotenuse.
Show answer
Hypotenuse c: 15
- Area of a circle with radius 7.
Show answer
Area: 153.93804
Frequently asked questions
Can a triangle have two right angles?
No. Two 90° angles already total 180°, leaving no room for a third.
Is an equilateral triangle also isosceles?
Yes, under the inclusive definition, because it has at least two equal sides.
How do I find the third angle?
Subtract the other two from 180°.
What is an obtuse triangle?
A triangle with one angle greater than 90°.
Try it yourself
Triangle CalculatorSolve any triangle from three sides, two sides and an angle, or two angles and a side.Pythagorean Theorem CalculatorFind the hypotenuse or a missing leg of a right triangle, plus area, perimeter and angles.Geometry CalculatorArea, perimeter, circumference, volume and surface area of common shapes.Keep learning
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