Question

an equilateral triangle has a semi - perimeter 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 the side - length of the equilateral triangle

Since the semi - perimeter $s = 6$ m and for an equilateral triangle $s=\frac{3a}{2}$ (where $a$ is the side - length), then $a=\frac{2s}{3}$. Substituting $s = 6$ m, we get $a=\frac{2\times6}{3}=4$ m.

Step2: Apply Heron's formula

Heron's formula is $A=\sqrt{s(s - a)(s - b)(s - c)}$. For an equilateral triangle $a=b = c$. Here, $s = 6$ m and $a=b = c = 4$ m. So $A=\sqrt{6(6 - 4)(6 - 4)(6 - 4)}=\sqrt{6\times2\times2\times2}=\sqrt{48}\approx7$ square meters.

Answer:

7 square meters