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6. An isosceles triangle has perimeter 30 cm arid each of the equal sides is 12 cm. Find the area of the triangle.
Answer :

sol: Let ?ABC be an isosceles triangle, in which,
We have, AB = AC = 12cm ...(Given)
image
Now, AB + AC + BC = 30 ...(Given, perimeter = 30cm)
i.e., 12 + 12 + BC = 30
i.e., BC = 30 - 24
So, BC = 6cm
Now, we know that, s=a+b+c2
Therefore, s=302=15cm

Now, Area of triangle = 15(15?12)(15?6)(15?12) ...(Since, Heron's formula [area = s(s?a)(s?b)(s?c)])
= 15×3×9×3
= 3×5×9×9
= 915cm2