Question

Find the area of isosceles triangle one of its equal sides is 'a' and other side is 'b' using herons formula

Answer 1

Step-by-step explanation:

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Answer 2

${semi perimeter = \frac{a + a + b}{2} = \frac{2a + b}{2} = a + \frac{b}{2} herons formula = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{(a + \frac{b}{2} )(a + \frac{b}{2} - a)(a + \frac{b}{2} - a)(a + \frac{b}{2} - b}) \\ \\ = \sqrt{(a + \frac{b}{2})( \frac{b}{2} )( \frac{b}{2})(a - \frac{b}{2} ) } \\ \\ = \frac{b}{2} \sqrt{ {a}^{2} - { (\frac{b}{2}) }^{2} } \\ \\ = \frac{b}{2} \sqrt{ {a}^{2} - \frac{ {b}^{2} }{4} \\ \\ = \frac{b}{2} \sqrt{ \frac{4 {a}^{2} + {b}^{2} }{4} } \\ \\ = \frac{b}{4} \sqrt{4 {a}^{2} - {b}^{2} }$