The area of a triangle can be computed using the lengths of the three sides of the triangle.The technique is called Heron's method and has been known for a long time. The formula is credited to Heron (or Hero) of Alexandria, and a proof can be found in his book, Metrica, written c. CE 60. It has been suggested that Archimedes knew the formula over two centuries earlier, and since Metrica is a collection of the mathematical knowledge available in the ancient world, it is possible that the formula predates the reference given in that work. (Source: https://en.wikipedia.org/wiki/Heron%27s_formula#History)
Let the lengths of the sides of a triangle be a, b, and c. Compute s = (1/2)*(a + b+ c), then the area A of the triangle is computed from the expression A = sqrt(s*(s - a)*(s - b)*(s - c)). (NOTE: the data displayed below uses pixel scale.)
You can check your work using that the total area of the yellow and green triangles is 28,500 while the total area of the red and black triangles is 20,000. (You may need to round the values from a calculator.)
David R. Hill