Q6 of 97 Page 790

Find the area of an isosceles triangle each of whose equal side is 13 cm and whose base is 24 cm.

Given:


Side AB = Side AC = 13 cm


Base = 24 cm



In ∆ADC (right-angled),


DC = 12 cm


By Pythagoras theorem,


AD2 + DC2 = AC2


⇒ AD2 = AC2 - DC2


⇒ AD2 = 132 - 122


⇒ AD2 = 169 – 144 = 25


⇒ AD = 5 cm


Now,


Area of triangle = 1/2 × base × height


= 1/2 × BC × AD


= 1/2 × 24 × 5


= 60 cm2


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