Question

The sides of a triangular field are 15 m, 20 m and 25 m. Find the area of
the triangle. ​

Answer 1

Given that , The three sides of a triangular field are 15 m, 20 m and 25 m.

Need To Find : Area of the Triangular Field ?

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⠀⠀⠀⠀⠀¤ Finding Semi Perimeter of Triangular field to find Area of Triangular Field :

As , We know that ,

• Formula for Semi-Perimeter of Triangle :

$\qquad \star \:\:\underline {\boxed {\pink{\pmb{\frak{ \:\:Semi\:Perimeter _{(\:Triangle \:)}\:(\:s\:) \:=\:\dfrac{ \: a + b + c }{2} \: \:\:units\:}}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Here , a , b & c are three sides of Triangular field .

$\dashrightarrow \sf \:\:Semi\:Perimeter _{(\:Triangle \:)}\:(\:s\:) \:=\:\dfrac{ \: a + b + c }{2} \: \:\:units\:\:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\dashrightarrow \sf \:\:Semi\:Perimeter _{(\:Triangle \:)}\:(\:s\:) \:=\:\dfrac{ \: a + b + c }{2} \: \:\\\\\dashrightarrow \sf \:\:Semi\:Perimeter _{(\:Triangle \:)}\:(\:s\:) \:=\:\dfrac{ \: 15 + 20 + 25 }{2} \: \:\\\\ \dashrightarrow \sf \:\:Semi\:Perimeter _{(\:Triangle \:)}\:(\:s\:) \:=\:\dfrac{ \: 60 }{2} \: \:\\\\\dashrightarrow \sf \:\:Semi\:Perimeter _{(\:Triangle \:)}\:(\:s\:) \:=\:\cancel{\dfrac{ \: 60 }{2}} \: \:\\\\\dashrightarrow \sf \:\:Semi\:Perimeter _{(\:Triangle \:)}\:(\:s\:) \:=\:30 \: \:\\\\ \dashrightarrow \underline {\boxed {\purple {\pmb{\purple {\:\:\:\:Semi\:Perimeter _{(\:Triangle \:)}\:(\:s\:) \:=\:30 \: \:m \:}}}}}\:\:\bigstar$

• Semi Perimeter of Triangular field is 30 m .

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⠀⠀⠀⠀⠀¤ Finding Area of Triangular Field :

As , We know that ,

• Formula Area of Triangle :

$\qquad \star \:\:\underline {\boxed {\pink{\pmb{\frak{ \:\:Area _{(\:Triangle \:)}\: \:=\:\sqrt{ s ( s - a ) ( s - b )( s - c)} \: \:\:sq.units\:}}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Here , a , b & c are three sides of Triangular field & s is the Semi-Perimeter of Triangular Field.

$\dashrightarrow \sf \:\:\:\:Area _{(\:Triangle \:)}\:\:=\:\sqrt{ s ( s - a ) ( s - b )( s - c)} \: \:\:sq.units \: \:\:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\dashrightarrow \sf \:\:\:\:Area _{(\:Triangle \:)}\:\:=\:\sqrt{ s ( s - a ) ( s - b )( s - c)} \: \:\: \:\:\\\\ \dashrightarrow \sf \:\:\:\:Area _{(\:Triangle \:)}\:\:=\:\sqrt{ 30 ( 30 - 15 ) ( 30 - 20 )( 30 - 25)} \: \:\: \:\:\\\\ \dashrightarrow \sf \:\:\:\:Area _{(\:Triangle \:)}\:\:=\:\sqrt{ 30 ( 15 ) ( 10 )(5)} \: \:\: \:\:\\\\ \dashrightarrow \sf \:\:\:\:Area _{(\:Triangle \:)}\:\:=\:\sqrt{ 30 ( 750 )} \: \:\: \:\:\\\\ \dashrightarrow \sf \:\:\:\:Area _{(\:Triangle \:)}\:\:=\:\sqrt{ 22,500} \: \:\: \:\:\\\\ \dashrightarrow \sf \:\:\:\:Area _{(\:Triangle \:)}\:\:=\: 150 \: \:\: \:\:\\\\ \dashrightarrow \underline {\boxed {\purple {\pmb{\purple {\:\:\:\:\:Area _{(\:Triangle \:)}\:\:=\: 150 \:m^2\:\: \:}}}}}\:\:\bigstar$

$\qquad \therefore \:\:\underline {\sf Hence, \:Area \:of \:Triangular \:Field \: is \:\pmb{\bf 150 \;m^2 \:}}$

Answer 2

Answer:

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