SOLUTION: In the diagram attached below, what is the area of the shaded region? Diagram: https://imgur.com/a/GIFAlct

Algebra ->  Triangles -> SOLUTION: In the diagram attached below, what is the area of the shaded region? Diagram: https://imgur.com/a/GIFAlct      Log On


   



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

Diagram: https://imgur.com/a/GIFAlct

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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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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(1)  First find the second leg of the large triangle.

     It is  sqrt%2825%5E2+-+7%5E2%29 = sqrt%28576%29 = 24 meters.



(2)  So, the area of the large triangle is  %281%2F2%29%2A24%2A7 = 12*7 = 84 square meters.



(3)  The large triangle and the small triangle are similar, with the similarity coefficient k = 4%2F7  (smaller to larger).



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

         k%5E2%2A84 = %2816%2F49%29%2A84 = %2816%2A12%29%2F7 = 192%2F7 = 27 3%2F7 = 27.42857  square meters  (rounded).   ANSWER

Solved.