Answer:
7 m^2
Step-by-step explanation:
[tex] s = \dfrac{a + b + c}{2} [/tex]
[tex] A = \sqrt{s(s - a)(s - b)(s - c)} [/tex]
[tex] s = 6 [/tex]
[tex] \dfrac{a + b + c}{2} = 6 [/tex]
[tex] a = b = c [/tex]
[tex] \dfrac{a + a + a}{2} = 6 [/tex]
[tex] 3a = 12 [/tex]
[tex] a = b = c = 4 [/tex]
[tex] A = \sqrt{6(6 - 4)(6 - 4)(6 - 4)} [/tex]
[tex] A = \sqrt{6(2)^3 [/tex]
[tex] A = \sqrt{48} [/tex]
[tex] A = 6.92820... [/tex]
[tex] A = 7~m^2 [/tex]
Answer:
Option 2 is correct that is area of triangle is 7 m².
Step-by-step explanation:
Given: Equilateral Triangle is given.
Semi Perimeter of triangle = 6
To find: Area of the triangle
Let, Side of equilateral triangle be x
Semi Perimeter, s = [tex]\frac{x+x+x}{2}[/tex]
[tex]\frac{3x}{2}=6[/tex]
[tex]3x=12[/tex]
[tex]x=4[/tex]
By Heron's formula,
[tex]Area=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]=\sqrt{6(6-4)(6-4)(6-4)}[/tex]
[tex]=\sqrt{6\times2\times2\times2}[/tex]
[tex]=\sqrt{48}[/tex]
[tex]=4\sqrt{3}[/tex]
[tex]=4\times1.73[/tex]
[tex]=6.92[/tex]
[tex]=7\:m^2\:(approx.)[/tex]
Therefore, Option 2 is correct that is area of triangle is 7 m².
