Answer:
The correct option is: 83 m²
Step-by-step 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 <u>Pythagoras theorem</u> 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
<u>So, the height of the equilateral triangle</u>: 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
