The perimeter of equilateral triangle is 3 *(⁴√(16over3)) units. Determine the area of the triangle.

The perimeter of equilateral triangle is 3 *(⁴√(16over3))…

The perimeter of equilateral triangle is $3 *(^4{\sqrt{16\over3}})$ units. Determine the area of the triangle.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 1 unit².

Perimeter = 3 × (4 $\sqrt{\frac{16}{3}}$ )

Perimeter = 3 × (4 $\sqrt{\frac{16}{3}}$ ) = 12 $\sqrt{\frac{16}{3}}$ = 12 × ${\frac{16}{\sqrt3}}$ = 16 $\sqrt{3}$

Side = Perimeter/3 = (16 $\sqrt{3}$ )/3

Area = $\sqrt{3}$ /4 a² = $\sqrt{3}$ /4 ((16 $\sqrt{3}$ )/3)² = (64 $\sqrt{3}$ )/3 unit²