Triangle is equilateral then all sides are equals
to find the area of the triangle we need x, then we can find x dividing the triangle
and apply pythagoras because this triangle is right
[tex]a^2+b^2=h^2[/tex]
where a and b are sides of the triangle and h the hypotenuse
the replacing
[tex]x^2+2^2=4^2[/tex]
simplify
[tex]x^2+4=16[/tex]
solve for x subtracting 4 on both sides
[tex]\begin{gathered} x^2+4-4=16-4 \\ x^2=12 \end{gathered}[/tex]
and solve x using roots
[tex]\begin{gathered} \sqrt[]{x^2}=\sqrt[]{12} \\ \\ x=\sqrt[]{12} \end{gathered}[/tex]
the the height of the triangle is root of 12
Area of the triangle
we apply the formula
[tex]A=\frac{b\times h}{2}[/tex]
where b is the length of the base of the triangle and h the height
replacing
[tex]\begin{gathered} A=\frac{4\times\sqrt[]{12}}{2} \\ \\ A=2\sqrt[]{12}\approx6.9 \end{gathered}[/tex]
then the area of the triangle is 6.9 square miles
