The formula you need is called "Heron's formula".
Let $a, b$ and $c$ be the length of the 3 sides of the triangle.
The semi-perimeter of the triangle $$s =\frac{a+b+c}{2}$$
The area of the triangle $$A =\sqrt{s(s-a)(s-b)(s-c)}$$
I need to know how to calculate the height of a specific triangle in order to calculate the area. i know the base length (4.24m) and the side lengths, which are equal, (5.8m) and i cant get access to the original triangle to measure the height. is there some other way to calculate it without the area? /// also a formula for the area of a triangle without using height could be used in this situation too.
The formula you need is called "Heron's formula".
Let $a, b$ and $c$ be the length of the 3 sides of the triangle.
The semi-perimeter of the triangle $$s =\frac{a+b+c}{2}$$
The area of the triangle $$A =\sqrt{s(s-a)(s-b)(s-c)}$$
Alternatively the triangle is an isosceles triangle and in an isosceles triangle the altitude to the base is also the median, that means it bisects the base. Hence you will get a right triangle with hypotenuse 5.8 m and base 2.12 m, now use Pythagoras theorem and find the height of the triangle.