Answer:
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Heron's formula states that the area of a triangle with side lengths a, b, and c is:
- [tex]A= \sqrt{s(s-a)(s-b)(s-c)}[/tex], where s = (a + b + c)/2 s is the semi-perimeter of the triangle.
We have a triangle with side lengths:
- a = 11, b = 15, and c = 19.
We can first find the semi-perimeter:
- s = (a + b + c)/2
- s = (11 + 15 + 19)/2
- s = 22.5
Then we can plug this into Heron's formula to find the area:
- [tex]A=\sqrt{22.5(22.5-11)(22.5-15)(22.5-19)} =\sqrt{6792.1875} =82.41\ rounded[/tex]
So the area of the triangle is approximately 82.41 square units.
