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Area of Triangles

- Calculus
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Calculating the area of a triangle depends on the kind of triangle you have.

The area of a triangle can be found in two formulas:

- For all triangles, you can use the formula:

Triangle A is shown below (all lengths are in cm):

- The area of the triangle =

For most triangles, the base and height are used as shown above.

- For all non-angled triangles, the formula is

To use this formula, angle C needs to be between the two sides. You can remember this through the acronym SAS (Side, Angle, Side).

A triangle is shown below (all lengths are in cm)

What is the area of the triangle?

- First, label the sides of the triangles according to the formula.
- This is not a right-angled triangle. We can use the formula below.
- Area of the triangle =

For right-angled triangles, the height for the right-angled triangle in the formula is equivalent to the vertical side.

- When using the formula you might need to work out one of the sides to get two sides next to the angle. To do so, you need to use Pythagoras theorem, whereby

An equilateral triangle can be seen below (all lengths are in cm):

The formula for the area of the triangle is but the height is unknown. To work out the height, you need to rearrange and use Pythagoras theorem.

- To use Pythagoras theorem, you need to find a and c: c is the hypotenuse and therefore, c = 5; a is half the base and therefore a = 4.
- Substitute the values into Pythagoras theorem: = . Therefore, the height is 3.
- Substitute the values into the Area of a Triangle formula:

- The area of any triangle can be calculated using the formula
- For all non-right-angled triangles, you can also use the formula
- The acronym SAS is used to figure out what values should be substituted into

The area of the triangle is the amount of space that the triangle takes up.

More about Area of Triangles

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