The area (in cm²) of an equilateral triangle whose altitude from vertex is 12 cm, is:  

Given:

Altitude from vertex is 12 cm.

Formula used:

For an equilateral triangle, the altitude (h) is given by:

h = \(\dfrac{\sqrt{3}}{2} \times a\)

where a is the side of the triangle.

The area (A) of an equilateral triangle is given by:

A = \(\dfrac{\sqrt{3}}{4} \times a^2\)

Calculations:

Given h = 12 cm

⇒ 12 = \(\dfrac{\sqrt{3}}{2} \times a\)

⇒ a = \(\dfrac{12 \times 2}{\sqrt{3}}\)

⇒ a = \(\dfrac{24}{\sqrt{3}}\)

⇒ a = 8√3 cm

Now, using the area formula:

A = \(\dfrac{\sqrt{3}}{4} \times (8\sqrt{3})^2\)

⇒ A = \(\dfrac{\sqrt{3}}{4} \times 192\)

⇒ A = 48√3 cm²

∴ The correct answer is option 2.