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27.111 square units.

This is an isosceles triangle with legs 8 & 8 and base 14. It can be split into two right triangles with base 7, and hypotenuse 8, so the other leg (which will be the height) is √(8² - 7²) = √15.

So the area of the original triangle is (1/2)*base*height = (1/2)*(14)*(√15) = 7√15 = 27.111

The free app Universal Triangle Solver [see related link] calculates the missing information as long as you have 3 pieces of info (3 sides, 2 sides + angle, etc.) It will tell you if there is more than one solution. For a unique solution it gives the area. I typed in the 3 sides (8,8,14) and got the same solution.

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Q: What is the area of a triangle with two sides of length 8 and one side length 14?
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