Suman Mazumdar

Triangle ABC is an isosceles triangle with two equal sides

AB= 12 cm, AC= 12 cm, BC = x cm

perimeter of an triangle= sum of three sides

since it is an isosceles triangle, so in this case

30= 12+12+x

⇒x= 6cm

so the length of the side BC is 6 cm.

so in this way we find out the the length of all sides of triangle ABC, where AB= 12 cm, AC= 12 cm, and BC= 6 cm. Now draw a perpinduclar from point A in the line BC, let the middle point is P so in this way the length of BP and BC= 3 cm.

Now according to the pythagorus theorm we will find the length of AP

AB²= AP²+BP²

⇒144= AP²+9

⇒ AP= √135

so now area of triangle ABP= 1/2∗base*height

=1/2*3* √135

=3√135/2

so area of triangle ABC= 2* area of triangle ABP

= 2* 3√135/2

= 3√135

= 3*11.61

= 34.83 cm²

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