An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Solution and Explanation
Let the third side of this triangle be x.
Perimeter of triangle = 30 cm
\(⇒\) 30 = 12 + 12 + c
c = 30 - 24
c = 6 cm
Semi Perimeter (s) = \(\frac{P}{2}\) =\( \frac{\text{(a + b + c)}}{2}\)
s = \(\frac{30}{2}\)
s = 15 cm
Using Heron’s formula,
Area of a triangle = \(\sqrt{\text{s(s - a)(s - b)(s - c)}}\)
\(= \sqrt{\text{15(15 - 12)(15 -12)(15 - 6)}}\)
\(= \sqrt{15 × 3 × 3 × 9}\)
\(= \sqrt{1215}\)
\(= 9\sqrt{15} \) cm2
Area of the triangle \(= 9\sqrt{15} \) cm2
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