Question 149
In the city of Oropis there is a lake in the shape of a triangle with each of the three sides being part of the perimeter of a square shaped terrain with areas $370~\mathrm{m}^2$, $116~\mathrm{m}^2$ and $74~\mathrm{m}^2$, as in the figure below. The mayor of Oropis, Arnaldo, wants to calculate the lake area, but he doesn't know how. The mayor's assistant, Bernaldo, has an idea. It says that it is enough to find values of $a, b, c$ and $d$ that satisfy the geometric conditions of the second figure in which the shaded area is congruent to the lake. He states that after this the task will become much simpler. 
a) Determine integer values of $a, b, c$ and $d$ that satisfy the geometric conditions of Bernaldo's figure.
b) Determine the lake area.
a) Determine integer values of $a, b, c$ and $d$ that satisfy the geometric conditions of Bernaldo's figure.
b) Determine the lake area.