Question

4.Find the area of the triangle whose lengths of sides 12m,9m,15m by using herons formula? ​

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Sides of triangle = 12m , 9m , 15m

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Area = ?? ( using herons formulae )

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{Semi\: perimeter = \dfrac{ a + b + c }{3}}}}}$

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$\sf: \implies{\bold{ Semi\: perimeter = \dfrac{12 + 9 + 15 }{3}}}$

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$\sf: \implies{\bold{ Semi\: perimeter = \dfrac{ 36} {3}}}$

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$\sf: \implies{\bold{ Semi\: perimeter = 18 m}}$

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$\sf{\red{\boxed{\bold{area = \sqrt{ s( s - a )( s - b ) ( s - c )}}}}}$

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$\sf: \implies{\bold{ area = \sqrt{ 18( 18 - 12)( 18 - 9 ) ( 18 - 15 ) }}}$

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$\sf: \implies{\bold{ area = \sqrt{ 18\times 6 \times 9 \times 3 }}}$

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$\sf: \implies{\bold{ area = \sqrt{ 3 \times 3\times 2 \times 2\times 3\times 3 \times 3 \times 3 }}}$

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$\sf: \implies{\bold{ area = { 3\times 2 \times 3 \times 3 }}}$

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$\sf: \implies{\bold{ area = 54 cm^2}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Area of triangle having sides 12cm , 9cm , 15cm is 54cm^2

Answer 2

Answer:

54sq. m

Step-by-step explanation:

let a=12m

b=9m

c=15m

S=a+b+c/2

=12+9+15/2

=36/2

=18

area of the triangle =√s(s-a) (s-b) (s-c)

=18(18-12)(18-9)(18-15)

=18(6)(9)(3)

=√2 3 3 2 3 3 3 3

=√2 3 3 3

=54sq. m