Answer :
Using Heron's formula, the area of a triangle with side lengths of 17.8 cm, 12.3 cm, and 25.2 cm is approximately 96.9 square units. The closest option provided is 101.2 cm², making option B the correct answer.
To find the area of a triangle using Heron's formula, we first need to calculate the semi-perimeter of the triangle (s), which is half the sum of the lengths of its sides. Then, we can use the formula:
Area = √(s(s - a)(s - b)(s - c))
Given the lengths of the sides:
a = 17.8 cm
b = 12.3 cm
c = 25.2 cm
We can calculate the semi-perimeter (s) as follows:
s = (a + b + c) / 2
s = (17.8 + 12.3 + 25.2) / 2
s = 55.3 / 2
s = 27.65
Now, we can substitute the values into Heron's formula:
Area = √(27.65(27.65 - 17.8)(27.65 - 12.3)(27.65 - 25.2))
Simplifying further:
Area = √(27.65(9.85)(15.35)(2.45))
Area = √(9.85 * 15.35 * 2.45 * 27.65)
Area ≈ √(9389.25)
Area ≈ 96.9
Rounding to the nearest tenth, the area of the triangle is approximately 96.9 square units.However, the closest option is 101.2 cm², so that would be the most appropriate choice given the available options. So Option B is correct.
For more question on Heron's formula visit:
https://brainly.com/question/10713495
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