Question

Could someone please explain how to solve for the area?

Answer 1

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

`a^2+b^2=h^2`

where a and b are sides of the triangle and h the hypotenuse

the replacing

`x^2+2^2=4^2`

simplify

`x^2+4=16`

solve for x subtracting 4 on both sides

`\begin{gathered} x^2+4-4=16-4 \\ x^2=12 \end{gathered}`

and solve x using roots

`\begin{gathered} \sqrt[]{x^2}=\sqrt[]{12} \\ \\ x=\sqrt[]{12} \end{gathered}`

the the height of the triangle is root of 12

Area of the triangle

we apply the formula

`A=(b* h)/(2)`

where b is the length of the base of the triangle and h the height

replacing

`\begin{gathered} A=\frac{4*\sqrt[]{12}}{2} \\ \\ A=2\sqrt[]{12}\approx6.9 \end{gathered}`

then the area of the triangle is 6.9 square miles