## Sketch

## Calculating the perimeter of a triangle

To calculate the perimeter of a triangle, you need to add the length of all three sides. The formula is therefore

Perimeter = side a side b side c

**Example calculation:** 10cm 5cm 3cm = 18cm

It is important that you measure the lengths of the sides correctly and state them in the same unit. For example, if you have the length of side a in centimetres, but the length of side b is given in meters, you must convert one of the two lengths.

If you know the lengths of the three sides, you can easily calculate the perimeter of the triangle. If not, you may need to use one of the other formulas to find the missing size.

## Calculating the area of a triangle

To calculate the area of a triangle, you need the length of the base and the height of the triangle. The base is the side of the triangle on which the triangle stands and the height is the vertical line that runs from the tip of the triangle to the base.

The formula for the area is

Area = 0.5 x base x height

**Example calculation:** (3cm * 5cm) / 2 = 7.^{5cm2}

To apply this formula, you must first determine the length of the base and the height of the triangle. If you have a right-angled triangle, for example, you can simply calculate the height by choosing a cathetus as the base and then calculating the area using this formula.

If you do not have a right-angled triangle and no height is given, you may need to use other methods to calculate the area. One option is to divide the triangle into two right-angled triangles and then calculate the area of each sub-triangle. Then simply add the two areas together.

Another method is to use the Pythagorean theorem to calculate the height of the triangle. Pythagoras' theorem states: In a right-angled triangle, the square over the hypotenuse is equal to the sum of the squares over the cathets. So if you know the length of the two legs, you can calculate the length of the hypotenuse and then calculate the area using the formula for the area of a right-angled triangle.