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Q6.    An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

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The perimeter of an isosceles triangle is 30 cm (Given).

The length of the sides which are equal is12 cm.

Let the third side length be 'a cm'.

Then, Perimeter = a+b+c

\Rightarrow 30= a+12+12

\Rightarrow a = 6cm

So, the semi-perimeter of the triangle is given by,

s= \frac{1}{2}Perimeter =\frac{1}{2}\times30cm = 15cm

Therefore, using Herons' Formula, calculating the area of the triangle

A = \sqrt{s(s-a)(s-b)(s-c)}

= \sqrt{15(15-6)(15-12)(15-12)}

= \sqrt{15(9)(3)(3)}

= 9\sqrt{15}\ cm^2

Hence, the area of the triangle is 9\sqrt{15}cm^2.




Posted by

Ritika Kankaria

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