In an isosceles triangle ABC with AB = AC and AD is perpendicular to BC, if AD = 6 cm and the perimeter of ΔABC is 36 cm, then the area of ΔABC is:

48 cm²

We know that,

Area of right angled triangle = \(\frac{1}{2}\) × Base × Height

We have,

AB = AC and AD is perpendicular to BC

and, AD = 6 cm

perimeter of ΔABC is 36 cm

We have a triplet =

10 , 8 , 6

According to this triplet the perimeter of the triangle = 10 + 10 + 8 + 8 = 36 cm ( satisfied )

So, with the help of this triplet we can conclude that,

BD = 8 and the value of BC is = 16

So, the area of the triangle = \(\frac{1}{2}\) × 8 × 6 = 48 cm²