Question

an equilateral triangle has a semiperimeter of 6 meters. what is the area of the triangle? round to the nearest square meter. 2 square meters 7 square meters 20 square meters 78 square meters semiperimeter = 6 m herons formula: area = \sqrt{s(s - a)(s - b)(s - c)}

Explanation:

Step1: Find side length of equilateral triangle

A triangle's semiperimeter \( s=\frac{a + b + c}{2}\). For an equilateral triangle, \(a = b = c\), so semiperimeter \(s=\frac{3a}{2}\). Given \(s = 6\) meters, solve for \(a\):

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So each side \(a=b=c = 4\) meters.

Step2: Apply Heron's formula

Heron's formula: \( \text{Area}=\sqrt{s(s - a)(s - b)(s - c)}\). Substitute \(s = 6\), \(a = 4\), \(b = 4\), \(c = 4\):

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Rounded to the nearest square meter is \(7\).

Answer:

7 square meters