Question

Find the area of the equilateral triangle if a side is 8 squared root 3 m. Round to the nearest whole number. 67 m2 55 m2 28 m2 83 m2

Answer 1

The correct option is: 83 m²

Explanation:

Side of an equilateral triangle: a = 8√3 m

Area of a triangle = 1/2 × base × height

Here, the height of the triangle = the length of the perpendicular bisector

Therefore, using the Pythagoras theorem to calculate the length of the perpendicular bisector of an equilateral triangle

a² = b² + c²

Here, hypotenuse of the smaller triangle: a = 8√3 m

base of the smaller triangle: b = a ÷ 2 = 8√3 ÷ 2 m = 4√3 m

and perpendicular bisector: c = ?

∴ a² = b² + c²

⇒ (8√3)² = (4√3)² + c²

⇒ c² = (8√3)² - (4√3)² = 192 - 48 = 144

So, the height of the equilateral triangle: c = √144 m = 12 m

and base of the equilateral triangle = 8√3 m

Therefore, the area of the equilateral triangle = 1/2 × base × height = 1/2 × 8√3 m × 12 m = 48√3 m² ≈ 83 m²