Question

find out the area of an isosceles triangle whose base is a and equal sides of length b

Answer 1

Given  : We have isosceles triangle with sides a , b and b 

We know Heron's formula :

Area of triangle  = s(s − a)(s − b)(s − c)−−−−−−−−−−−−−−−−−−−√

Here

a  ,  b and c  are sides of triangle 

And

s  = a + b + c2

Here a =  a  ,  b  = b and c =  b  , So 

s  = a + b + b2 = a + 2b2

And

Area of given isosceles triangle :
⇒a + 2b2(a + 2b2 − a)(a + 2b2 − b)(a + 2b2 − b)−−−−−−−−−−−−−−−−−−−−−−−⎷ ⇒ a + 2b2(a + 2b − 2a2)(a + 2b − 2b2)(a + 2b − 2b2)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−⎷⇒ a + 2b2(b − a2)(a2)(a2)−−−−−−−−−−−−−−−−−√⇒ (a + 2b)( b −a)(a2)16−−−−−−−−−−−−√⇒ a(a + 2b)( b −a)√4⇒ a(ab − a2 + 2b2 − 2ab)√4⇒ a2b2 − a2 − ab√4                                                                         ⎛⎝⎜⎜⎜⎜⎜ Ans ⎞⎠⎟⎟⎟⎟⎟