Question

fall 2025 geometry b wwva area and perimeter of triangles an equilateral triangle has a semi - perimeter of 6 meters. what is the area of the triangle? round to the nearest square meter. herons formula: area =\sqrt{s(s - a)(s - b)(s - c)}

Explanation:

Step1: Find side - length of equilateral triangle

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

Step2: Use Heron's formula

Heron's formula for the area of a triangle is $A=\sqrt{s(s - a)(s - b)(s - c)}$. For an equilateral triangle $a=b = c$. So $A=\sqrt{s(s - a)^3}$. Substituting $s = 6$ m and $a = 4$ m, we have $A=\sqrt{6\times(6 - 4)^3}=\sqrt{6\times8}=\sqrt{48}\approx7$ square meters.

Answer:

7 square meters