Answer:
The lateral area is equal to
[tex]LA=64\sqrt{3}\ m^{2}[/tex]
Step-by-step explanation:
In this problem the lateral area is equal to the area of one equilateral triangle multiplied by [tex]4[/tex]
To find the area of one equilateral triangle calculate the height
The area of the triangle is equal to
[tex]A=\frac{1}{2}bh[/tex]
we have
[tex]b=8\ m[/tex]
Applying the Pythagoras theorem
[tex]h^{2}=8^{2} -4^{2} \\h^{2}=64-16\\ h=\sqrt{48} \\ h=4\sqrt{3}\ m[/tex]
The area of one triangle is equal to
[tex]A=\frac{1}{2}(8)(4\sqrt{3})\ m^{2}[/tex]
so
The lateral area is equal to
[tex]LA=4\frac{1}{2}(8)(4\sqrt{3})=64\sqrt{3}\ m^{2}[/tex]
