Let height of triangle = h cm

Given: Base of the triangle (b) = 12 cm

Equal sides (a) = h + 2 cm

Now,

Area of a triangle = 1/2 × Base × Height

And,

Area of isosceles triangle = 1/4 × b√(4a² – b²)

⇒ 1/2 × Base × Height = 1/4 × b√(4a² – b²)

⇒ 1/2 × 12 × h = 1/4 × 12√[4(h + 2)² – 12²]

⇒ 6h = 3√(4h² + 16h + 16-144)

⇒ 2h = √(4h² + 16h-128)

On squaring both sides we get,

⇒ 4h² = 4h² + 16h – 128

⇒ 16h – 128 = 0

⇒ 16h = 128

⇒ h = 8 cm

Now,

Area of a triangle = 1/2 × Base × Height

= 1/2 × 12 cm × 8 cm

= 1/2 × 96 cm²

= 48 cm²