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
herons formula: area = $sqrt{s(s - a)(s - b)(s - c)}$

Explanation:

Step1: Find side length

Semiperimeter \( s = 6 \, \text{m} \), perimeter \( = 2s = 12 \, \text{m} \). Equilateral triangle has 3 equal sides, so side \( a = \frac{12}{3} = 4 \, \text{m} \).

Step2: Apply Heron's formula

\( \text{Area} = \sqrt{s(s-a)(s-b)(s-c)} \). Since \( a = b = c = 4 \), \( s-a = s-b = s-c = 6-4=2 \). Thus, \( \text{Area} = \sqrt{6 \times 2 \times 2 \times 2} = \sqrt{48} \approx 6.928 \approx 7 \, \text{m}^2 \).

Answer:

B. 7 square meters