Question

Could someone please explain how to solve for the area?

Answer 1

9514 1404 393

Answer:

  6.9 m²

Step-by-step explanation:

All of the sides are the same length. The altitude meets the base at its midpoint, so the altitude (h) of the triangle can be found using the Pythagorean theorem.

  h² + 2² = 4²

  h² = 12

  h = 2√3

Then the area is ...

  A = 1/2bh

  A = (1/2)(4 m)(2√3 m) = 4√3 m² ≈ 6.9 m²

___

If you work through the above area formula in generic terms, you find the area of an equilateral triangle to be ...

  A = (s²/4)√3 . . . . . where s is the side length

Another approach is to treat the figure as a 3-gon and use the n-gon area formula that uses the perimeter. That formula is derived here brainly.com/question/22386162

It is ...

  A = P²/(4n·tan(180°/n))

For a triangle with side length s, this is ...

  A = (3s)²/(4·3·tan(60°) = (s²/4)√3 . . . . same as above

Answer 2

Answer:

area of equilateral TRAINGLE =√3/4 A²=√3/4×4²=6.9mi² is your answer