Created by Hanna Pamuła, PhD
Reviewed by
Bogna Szyk and Adena Benn
Last updated:
Jan 18, 2024
- Triangle area formula
- How to use this triangle area calculator?
- How do I calculate the area of an equilateral triangle?
- FAQ
This triangle area calculator can help in determining the triangle area. The basic triangle area formula needs to have a base and height given, but what if we don't have it? How can we calculate the area of a triangle with 3 sides only? The triangle area calculator is here for you. Give it a go! If you are still unsure how to find the area of a triangle, check the description below.
Triangle area formula
A triangle is one of the most basic shapes in geometry. The best known and the most straightforward formula, which almost everybody remembers from school, is:
area = 0.5 × b × h, wherebis the length of the base of the triangle, andhis the height/altitude of the triangle.
However, sometimes it's hard to find the height of the triangle. In that cases, many other equations may be used, depending on what you know about the triangle:
Three sides (SSS)
If you know the lengths of all sides, use the Heron's formula:
area = 0.25 × √( (a + b + c) × (-a + b + c) × (a - b + c) × (a + b - c) )
Two sides and the angle between them (SAS)
See AlsoCofactor Expansion CalculatorYou can calculate the area of a triangle easily from trigonometry:
area = 0.5 × a × b × sin(γ)
Two angles and a side between them (ASA)
There are different triangle area formulas versions - you can use, for example, trigonometry or law of sines to derive it:
area = a² × sin(β) × sin(γ) / (2 × sin(β + γ))
If you are looking for other formulas or calculators connected with triangles, check out this right triangle calculator, pythagorean theorem calculator, and law of cosines calculator.
How to use this triangle area calculator?
Assume that we know two sides and the angle between them:
- Type the first side length. It can be equal to 9 inches in our example.
- Determine the angle between two known sides. For example, 30 degrees.
- Enter the second triangle side. Let's choose 5 in.
- Watch our triangle area calculator performing all calculations for you! The area for our case is equal to 11.25 in².
How do I calculate the area of an equilateral triangle?
To calculate the area of an equilateral triangle, you only need to know the side:
area = a² × √3 / 4
Since √3 / 4 is approximately 0.433, we can formulate a quick recipe: to approximate the area of an equilateral triangle, square the side's length and then multiply by 0.433.
Although we prepared a separate calculator for the equilateral triangle area, you can quickly calculate it in this triangle area calculator. Simply use the subpart for the area of a triangle with 3 sides - as you know, every side has the same length in an equilateral triangle. It's possible to calculate that area also in the angle-side-angle or side-angle-side version - you probably remember that every angle in the equilateral triangle is equal to 60 degrees (π/3 rad).
FAQ
How do I find the area of a triangle given sides?
If you know the lengths of all sides (a, b, and c) of a triangle, you can compute its area:
- Calculate half of the perimeter
½(a + b + c). Denote this value bys. - Compute
s - a,s - b, ands - c. - Multiply the three numbers from Step 2.
- Multiply the result by
s. - Take the square root of the result.
- This is the area of your triangle - well done! The method we've used is called Heron's formula.
How do I find the area of a triangle given angles?
You can't determine the area of a triangle if you know only the angles. This is because there are infinitely many triangles with the same angles. You must know at least one side (or height) of your triangle to determine its area.
How do I calculate the area of a right triangle?
To compute the area of a right triangle, you only need to multiply the lengths of the legs of your triangle and then divide the result by 2. For instance, if the legs are 3 in and 4 in, then the area is 3 × 4 /2 = 12 / 2 = 6 in sq.
What is the area of an equilateral triangle of side 10?
The area is approximately 43.3. The precise answer is 25 × √3. To get this answer, recall the formula for the area of an equilateral triangle of side a reads area = a2 × √3 / 4. For the triangle with side 10 we obtain area = 102 × √3 / 4 = 100 × √3 / 4 = 25 × √3, which is approximately equal to 43.3.
Hanna Pamuła, PhD
