Question 1189709
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In the diagram attached below, what is the area of the shaded region?

Diagram: https://imgur.com/a/GIFAlct
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<pre>
(1)  First find the second leg of the large triangle.

     It is  {{{sqrt(25^2 - 7^2)}}} = {{{sqrt(576)}}} = 24 meters.



(2)  So, the area of the large triangle is  {{{(1/2)*24*7}}} = 12*7 = 84 square meters.



(3)  The large triangle and the small triangle are similar, with the similarity coefficient k = {{{4/7}}}  (smaller to larger).



(4)  THEREFORE, the area of the small triangle (shaded area) is  

         {{{k^2*84}}} = {{{(16/49)*84}}} = {{{(16*12)/7}}} = {{{192/7}}} = 27 {{{3/7}}} = 27.42857  square meters  (rounded).   <U>ANSWER</U>
</pre>

Solved.