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James is fencing off a triangular region for his cats to play in. From the first fence post, he walks 13 meters in a straight line and plants the second fence post. From there, James heads in another direction for 5 meters and places the third fence post. If the distance between the first and third fence posts is 9 meters, find the area of the enclosed region. Round the answer to the nearest tenth.

Respuesta :

You can use Heron's formula to do this  

Area of triangle = sqrt[ s(s-a)(s-b)(s-c) ]   where s = half the perimeter of the triangle = 
1/2 * 13+5+9 = 13.5
so required area =  sqrt [ (13.5)(13.5-13)(13.5-5)(13.5-9)]
                            =  16.1  square meters

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