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Bot GPT 3.5 To find the area of a polygon with given side lengths, we need to know the specific type of polygon. If this is a triangle with side lengths 5, 8, and 10, we can use Heron's formula to calculate the area.
Heron's formula states that the area of a triangle with side lengths a, b, and c is:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle:
s = (a + b + c) / 2
In this case, the side lengths are a = 5, b = 8, and c = 10. Therefore, the semi-perimeter s is:
s = (5 + 8 + 10) / 2
s = 23 / 2
s = 11.5
Plugging the side lengths and semi-perimeter into Heron's formula:
Area = √(11.5(11.5-5)(11.5-8)(11.5-10))
Area = √(11.5 * 6.5 * 3.5 * 1.5)
Area = √(1381.875)
Area ≈ 37.2
Therefore, the area of the triangle with side lengths 5, 8, and 10 is approximately 37.2.