Question

If the height of an equilateral triangle is 5.382 inches, what is its area?

Answer 1

`color(white)(xxx)9.655308*sqrt3`

Explanation:

Let a be length of one side of the triangle:

`color(white)(xx)sqrt3*a/2=h`
`=>sqrt3*a/2=5.382`
Multiply both side by `2/sqrt3`
`color(white)(xx)color(red)(2/sqrt3*)sqrt3*a/2=color(red)(2/sqrt3*)5.382`

`=>a=5.382*2/sqrt3`
Multiply both numerator and denominator by `sqrt3`
`color(white)(xxx)=5.382*2/sqrt3color(blue)(*sqrt3/sqrt3)`
`color(white)(xxx)=2*1.794sqrt3`

`color(white)(xx)A=ah/2`
`color(white)(xxx)=2*1.794*sqrt3*5.382*1/2`
`color(white)(xxx)=9.655308*sqrt3`