Q6 of 16 Page 133

The base (unequal side) of an isosceles triangle is 4 cm and its perimeter is 20 cm. Find its Area.

We have


Given: BC = 4 cm


Perimeter = 20 cm


Let the equal sides be x cm each.


Then, perimeter of an isosceles triangle is given by


AB + BC + CA = Perimeter


⇒ x + 4 + x = 20


⇒ 2x + 4 = 20


⇒ 2x = 20 – 4


⇒ 2x = 16



⇒ x = 8


Let the sides be


a = AB = 8 cm


b = CA = 8 cm


c = BC = 4 cm


Area of an isosceles triangle is given as,



Where


Here,



⇒ s = 10


And a = 8 cm, b = 8 cm and c = 4 cm.


So,


Area = √[10(10 – 8)(10 – 8)(10 – 4)]


⇒ Area = √(10 × 2 × 2 × 6)


⇒ Area = √(2 × 5 × 2 × 2 × 2 × 3)


⇒ Area = 4 √15 cm2


Thus, the area of the isosceles triangle is 4 √15 cm2.


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