Scalene Triangle Calculator

A Scalene Triangle Calculator helps you quickly calculate the area, perimeter, semiperimeter, and angles of a triangle when all three side lengths are known. Simply enter the sides a, b, and c, and the calculator instantly determines the triangle’s measurements.

A scalene triangle is a triangle where all three sides have different lengths and all angles are different. Because none of the sides are equal, general formulas such as Heron’s formula and the Law of Cosines are used to calculate its properties.

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What Is a Scalene Triangle?

A scalene triangle is a triangle in which all three sides are different.

• All sides have different lengths
• All interior angles are different
• No sides are equal
• No line of symmetry exists

The sum of the interior angles of any triangle is:

\( A + B + C = 180^\circ \)

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Scalene Triangle Formulas

1. Perimeter Formula

The perimeter of a scalene triangle is the sum of all three sides.

\( P = a + b + c \)

Where:

• a, b, c = lengths of the triangle sides

2. Semiperimeter Formula

The semiperimeter is half of the triangle’s perimeter.

\( s = \frac{a + b + c}{2} \)

3. Area Formula (Heron's Formula)

The area of a scalene triangle can be calculated using Heron's formula.

\( Area = \sqrt{s(s-a)(s-b)(s-c)} \)

Where:

• s = semiperimeter
• a, b, c = side lengths

4. Angle Formula (Law of Cosines)

Angles of a scalene triangle are calculated using the Law of Cosines.

\( A = \cos^{-1}\left(\frac{b^2 + c^2 - a^2}{2bc}\right) \)

\( B = \cos^{-1}\left(\frac{a^2 + c^2 - b^2}{2ac}\right) \)

\( C = 180^\circ - A - B \)

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Example Calculation

Suppose the triangle sides are:

• a = 5
• b = 6
• c = 7

Step 1: Perimeter

\( P = 5 + 6 + 7 = 18 \)

Step 2: Semiperimeter

\( s = \frac{18}{2} = 9 \)

Step 3: Area

\( Area = \sqrt{9(9-5)(9-6)(9-7)} \)

\( Area = \sqrt{216} \approx 14.7 \)

Step 4: Angles

Using the Law of Cosines:

• A ≈ 44.4°
• B ≈ 57.1°
• C ≈ 78.5°

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Triangle Inequality Rule

For three sides to form a triangle, they must satisfy thetriangle inequality rule.

\( a + b > c \)

\( b + c > a \)

\( a + c > b \)

If these conditions are not satisfied, the triangle cannot exist.

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Applications of Scalene Triangles

Scalene triangles appear in many real-world applications:

• Architecture and construction
• Engineering design
• Surveying and navigation
• Computer graphics and geometry
• Physics and mechanical calculations

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FAQ on Scalene Triangle Calculator

What is a scalene triangle?

A scalene triangle is a triangle in which all three sides and all three angles are different.

Can a scalene triangle be a right triangle?

Yes. A triangle can be both scalene and right-angled if one angle equals 90° and all sides are different.

How do you calculate the area of a scalene triangle?

The area is calculated using Heron's formula:

\( Area = \sqrt{s(s-a)(s-b)(s-c)} \)

What is the difference between scalene and isosceles triangles?

Triangle Type	Description
Scalene	All sides are different
Isosceles	Two sides are equal
Equilateral	All sides are equal

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