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Square Feet of a Triangle Calculator

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How do I use the square feet of a triangle calculator?How do I calculate the square feet of a triangle?Related calculatorsFAQs

Welcome to the square feet of a triangle calculator, where we'll explain all there is to know about how to calculate the square feet of a triangle. Let's get to the point and calculate some triangles' square feet!

How do I use the square feet of a triangle calculator?

Using the square feet of a triangle calculator is easy! Follow these steps:

  1. Select what you know about the triangle from the list. You can find the square feet of triangles if you know the following combination of length and angles:

    • Base and height;
    • Three sides (SSS);
    • Side-angle-side (SAS); and
    • Angle-side-angle (ASA).

  2. Enter the measurements of the triangle type you've selected. Refer to the schematic if you're unsure which measurements correspond to which fields.

  3. Let the square feet of a triangle calculator automatically find the area of the triangle.

If you want to learn how to find the square feet of a triangle by yourself, then keep scrolling!

How do I calculate the square feet of a triangle?

It depends on what measurements of the triangle you already know. Most commonly, you'd have one of these sets of measurements at your disposal:

  • Base and height;
  • Three sides (also called SSS);
  • Side-angle-side (SAS); or
  • Angle-side-angle (ASA).

Let's look at each triangle type and see how we can calculate its area, AA.

Base and height

Triangle area: triangle with base and height
A triangle with its base and height known.

The base and height triangle area formula simply uses the base bb and the height hh:

A=12×b×h\footnotesize A = \frac{1}{2}×b×h

Three sides

Triangle area: triangle with three sides
An SSS triangle with all three sides known.

When all three sides aa, bb, and cc are known, we can use Heron's formula,

A=s(s−a)(s−b)(s−c)\footnotesize A = \sqrt{s(s-a)(s-b)(s-c)}

where ss is the semiperimeter, s=12(a+b+c)s = \tfrac{1}{2}(a+b+c).

Side-angle-side

Triangle area: triangle with two sides and angle between them (SAS)
An SAS triangle with two sides and the angle in-between them known.

The SAS triangle has two sides aa and bb known, as well as the angle γ\gamma that lies in-between aa and bb. Its area formula is pretty simple:

A=a×b×sin⁡(γ)\footnotesize A = a \times b \times \sin(\gamma)

Angle-side-angle

Triangle area: triangle with two angles and side between them (ASA)
An ASA triangle with two angles and the side in-between them known.

The ASA triangle has two angles γ\gamma and β\beta known, as well as the side aa in-between these angles. You can work out its area with:

A=a2×sin⁡(β)×sin⁡(γ)2×sin⁡(β+γ)\footnotesize A = \frac{a^2 \times \sin(\beta) \times \sin(\gamma)}{2 \times \sin(\beta + \gamma)}
FAQs

What is the square feet area of a triangle with sides of 6 feet?

Its area is 15.59 ft². Since we know that all three sides are 6 feet long, we can use Heron's formula to work out its area in square feet.

  1. Calculate the perimeter:
    p = 3 × (6 ft) = 18 ft
  2. Divide the perimeter in half to get the semiperimeter:
    s = ½p = 9 ft
  3. Use Heron's formula:
    A = √[ s(s−a)(s−b)(s−c) ]
    A = √[ 9 × (9 − 6)³ ]
    A = √[ 9 × (3)³ ]
    A = 15.59 ft²

How do I determine the square feet of scalene triangle?

If you know it's a scalene triangle, then chances are you already know its side lengths. In that case, you can use Heron's formula to determine the triangle's area:

A = √[ s(s−a)(s−b)(s−c) ]

Here, s is the semiperimeter, which is half of the triangle's perimeter.

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Triangle area: triangle with base and height.
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