Find the area of the triangle whose sides are 18cm, 24cm and 30 cm. Also, find the height corresponding to the smallest side.

Given: Side 1 = a (let) = 18 cm

Side 2 = b (let) = 24 cm

Side 3 = c (let) = 30 cm

We know that,

Area of a scalene triangle = √(s(s-a)(s-b)(s-c))

Where,

⇒ s = 36 cm

Now,

Area of a scalene triangle = √(36cm × (36-18)cm × (36-24)cm × (36-30)cm)

= √(36cm × 18cm × 12cm × 6cm)

= √46656 cm²

= 216 cm²

Clearly,

Length of smallest side = 18 cm

Now,

We know that,

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

⇒ 216 cm²= 1/2 × 18 cm × Height

⇒ 216 cm²= 9 cm × Height

⇒ Height = 24 cm