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Scalene Triangle Area Calculator

Created by Aleksandra Zając, MD
Reviewed by Steven Wooding
Last updated: Jan 18, 2024


Triangles are ubiquitous in geometry, but you're in the right place if you're looking for something about scalene triangles particularly. Scalene triangle area calculator will help you find the area of the figure no matter what data you have given. Sides? Angles? Height and base? – we've covered them all with special scalene triangle area formulas. Read on and get to know more about triangles!

What is a scalene triangle?

A scalene triangle is a triangle with three sides, all of different lengths. There are no two or three sides of the same length in a scalene triangle.

Using scalene triangle area calculator

Using our tool is simple & intuitive!

  1. In the first row, choose the mode you want to work in. It depends on which data about your triangle you know.
  2. Let's assume we know the three sides, so we choose the mode three sides SSS (side-side-side).
  3. Under the triangle image, we can see three empty fields. Input the lengths of the sides.
  4. Our calculator works automatically and gives you the answer right away.
  5. To use a different mode, just choose it in the first row. No need to clear the data.
  6. Now you know how to use the scalene triangle area calculator!
  7. Remember that all the scalene triangle area formulas are available in the text below in case you need them.

How do I find the area of the scalene triangle? – formulas

There are four ways to find the area of a scalene triangle. The use depends on which data you have given.

Scalene triangle area formulas with known:

  1. Base (bb) and height (hh)
area=12×b×h\footnotesize\quad \text{area}=\frac{1}{2} \times b \times h
  1. Three sides (aa, bb, cc)
area=14×(a+b+c) ×(a+b+c)(ab+c) ×(a+bc)\footnotesize\quad \begin{align*} \text{area} &= \frac{1}{4} \times \sqrt{(a+b+c)}\ \times\\[1em] &\quad\sqrt{(-a+b+c)(a-b+c)}\ \times\\[1em] &\quad\sqrt{(a+b-c)} \end{align*}
  1. Two sides and the angle between them (sides – aa, bb; angle – γ\gamma)
area=12×a×b×sin(γ)\footnotesize\quad \text{area}=\frac{1}{2} \times a \times b \times \sin(\gamma)
  1. Two angles (γ\gamma, β\beta) and a side between them (aa)
area=a2×sin(β)×sin(γ)2×sin(β+γ)\footnotesize\quad \text{area} = a^2\! \times \sin(\beta)\! \times\! \frac{\sin(\gamma)}{2\! \times \sin(\beta + \gamma)}

FAQ

Are all scalene triangles acute?

No, not all scalene triangles are acute. A scalene triangle might be right, acute, or obtuse.

How do I calculate the scalene triangle area?

To calculate the scalene triangle area, use one of these equations:

  1. area = 0.5 × b × h, where b – the base, h – height.
  2. area = 0.25 × √[(a + b + c)(-a + b + c)(a - b + c)(a + b - c)], where a, b, c – triangle's sides.
  3. area = 0.5 × a × b × sin(γ), where a, b - sides; γ – an angle between those sides.
  4. area = a² × sin(β) × sin(γ) / (2 × sin(β + γ)), where β, γ – angles, a – side between those angles.

How do I find the area of the scalene triangle with sides 3, 5, 7 inches?

The area of this triangle is 6.495 in2. To find the triangle area with three sides:

  1. Use Heron's formula:
    area = 0.25 × √[(a + b + c)(-a + b + c)(a - b + c)(a + b - c)]
  2. Knowing all three a, b, c, solve the equation.
  3. The answer is 6.495 in2.

How many sides are equal in a scalene triangle?

There are no equal sides in a scalene triangle. A scalene triangle is a triangle with three unequal sides.

Aleksandra Zając, MD
Given
three sides (SSS)
Triangle area: triangle with three sides





a
in
b
in
c
in
Area
in²
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