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Find the area of an isocelas …

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Find the area of an isocelas tringleusing herons let lenth of equal side a and base as b

Posted by Micro Max Chamoli 7 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Rashmi Bajpayee 7 years, 10 months ago

s = ${{a + a + b} \over 2} = {{2a + b} \over 2}$

Now, Area of triangle = $\sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)}$

= $\sqrt {{{2a + b} \over 2}\left( {{{2a + b} \over 2} - a} \right)\left( {{{2a + b} \over 2} - a} \right)\left( {{{2a + b} \over 2} - b} \right)}$

= $\sqrt {{{2a + b} \over 2}\left( {{{2a + b - 2a} \over 2}} \right)\left( {{{2a + b - 2a} \over 2}} \right)\left( {{{2a + b - 2b} \over 2}} \right)}$

= $\sqrt {{{2a + b} \over 2}\left( {{b \over 2}} \right)\left( {{b \over 2}} \right)\left( {{{2a - b} \over 2}} \right)}$

= $\sqrt {{{4{a^2} - {b^2}} \over 4}{{\left( {{b \over 2}} \right)}^2}}$

= ${b \over 4}\sqrt {4{a^2} - {b^2}}$

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