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Heron’s Formula
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22/07/2021 11:01 am
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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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22/07/2021 11:04 am
First, let the third side be x.
It is given that the length of the equal sides is 12 cm and its perimeter is 30 cm.
30 = 12 + 12 + x
∴ The length of the third side = 6 cm
Thus, the semi perimeter of the isosceles triangle (s) = 30/2 cm
= 15 cm
Using Heron’s formula,
Area of the triangle
= \(\sqrt{s(s - a)(s - b)(s - c)}\)
= \(\sqrt{15(15 - 12)(15 - 12)(15 - 6)}cm^2\)
= \(\sqrt{15 \times 3 \times 3 \times 9}cm^2\)
= 9\(\sqrt{15}cm^2\)