Question
Find the area of a triangle whose sides are respectively 9cm, 12cm and 15cm.
✓
Answer
Let the sides of the given triangle be a, b, c respectively. So given, a = 9cm b = 12cm c = 15cm By using Heron's Formula The area of the triangle $=\sqrt{\text{s}\times(\text{s}-\text{a})\times(\text{s}-\text{b})\times(\text{s}-\text{c})}$ Semi perimeter of a triangle = s 2s = a + b + c$\text{s}=\frac{\text{a}+\text{b}+\text{c}}{2}$
$\text{s}=\frac{(9+12+15)}{2}$
$\text{s} = 18\text{cm}$
$\therefore$ Area of the triangle $=\sqrt{\text{s}\times(\text{s}-\text{a})\times(\text{s}-\text{b})\times(\text{s}-\text{c})}$
$=\sqrt{18\times(18-9)\times(18-12)\times(18-15)}$
$= 54\text{cm}^2$
$\text{s}=\frac{(9+12+15)}{2}$
$\text{s} = 18\text{cm}$
$\therefore$ Area of the triangle $=\sqrt{\text{s}\times(\text{s}-\text{a})\times(\text{s}-\text{b})\times(\text{s}-\text{c})}$
$=\sqrt{18\times(18-9)\times(18-12)\times(18-15)}$
$= 54\text{cm}^2$
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