There are three squares and one triangle in the figure above. The side lengths of squares are AB, BC and CA. The number within each square is the area of each square. Find the area of the triangle ABC.


 May 28, 2020

I would use Heron's formula for the area of a triangle:

--  if ab, 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 - a) · (s - b) · (s - c) )


To find ab, 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.

 May 28, 2020

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