Let the radius of base be ‘r’ km and slant height be ‘l’ km

Slant height of conical mountain = 2.5 km

Area of its base = 1.54 km²

Area of base is given by πr²

∴ πr² = 1.54 km²

⇒ 22/7 × r² = 1.54 km²

⇒ r² = 1.54 × 7/22 km² = .49 km²

⇒ r = 0.7 km

Let ‘h’ be the height of the mountain

We know,

l² = r² + h²

Substituting the values of l and r in the above equation

2.5² = 0.7² + h²

h² = 2.5² – 0.7² = 6.25 – 0.49 km²

h² = 5.76 km²

h = 2.4 km

∴ Height of the mountain = 2.4 km