Last updated: Apr 28, 2024

Square Feet of a Triangle Calculator

Q: 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. Calculate the perimeter: p = 3 × (6 ft) = 18 ft Divide the perimeter in half to get the semiperimeter: s = ½p = 9 ft 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 Read more

Table of contents

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

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:

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

Base and height

The base and height triangle area formula simply uses the base $b$ and the height $h$ :

\footnotesize A = \frac{1}{2}×b×h

Three sides

When all three sides $a$ , $b$ , and $c$ are known, we can use Heron's formula,

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

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

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 $a$ and $b$ known, as well as the angle $\gamma$ that lies in-between $a$ and $b$ . Its area formula is pretty simple:

\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 $\gamma$ and $\beta$ known, as well as the side $a$ in-between these angles. You can work out its area with:

\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.

Calculate the perimeter:
p = 3 × (6 ft) = 18 ft
Divide the perimeter in half to get the semiperimeter:
s = ½p = 9 ft
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.