Find the area of the triangle described below. Round to the nearest hundredth.a=6𝑎=6, c=27𝑐=27, b=26
Question
Find the area of the triangle described below. Round to the nearest hundredth.a=6𝑎=6, c=27𝑐=27, b=26
Solution
To find the area of a triangle using the lengths of three sides, you can use Heron's formula. Here are the steps:
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Calculate the semi-perimeter of the triangle. The semi-perimeter (s) is half the sum of the lengths of the sides (a, b, and c). So, s = (a + b + c) / 2 = (6 + 26 + 27) / 2 = 29.5.
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Use Heron's formula to find the area. The formula is √[s(s - a)(s - b)(s - c)]. So, the area = √[29.5(29.5 - 6)(29.5 - 26)(29.5 - 27)].
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Calculate the value inside the square root: 29.5 * 23.5 * 3.5 * 2.5 = 4861.25.
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Take the square root of 4861.25 to find the area. The area ≈ 69.72 (rounded to the nearest hundredth).
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