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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
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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 https://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
