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