I would use Heron's formula for the area of a triangle:
-- if a, b, and c are the sides of a triangle:
-- first find the semiperimeter, s, by using this formula: s = (a + b + c) / 2
-- and then find the area by using this formula: area = sqrt( s · (s - a) · (s - b) · (s - c) )
To find a, b, and c -- find the square roots of the areas of the squares to find their side lengths:
-- a = sqrt(116)
-- b = sqrt(370)
-- c = sqrt(74)
Although there may be a way to do this without a calculator, I would suggest using one ... preferably one that allows
you to store and recall values.
Interestingly, the result is a whole number.