Question

The area of the triangular field. if sides of the triangular field are 325m, 300m, 125m?

Answer 1

Answer:

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Answer 2

★ Required answer:-

• Area of the triangular field is 18750 m².

★ Given:-    

• Length of side a = 325m
• Length of side b = 300m
• Length of side c = 125m

★To find:-    

• Area of the triangle

★ Formula used:-    

• $\boxed{\sf{Semi\:-\:perimeter\:=\:\dfrac{a\:+\:b\:+c}{2}}}$

Where,

• a = Length of side a = 325m
• b = Length of side b = 300m
• c = Length of side c = 125m

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad}$

• $\boxed{\sf{Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{s\:(\:s\:-\:a\:)\:(\:s\:-\:b\:)\:(\:s\:-\:c\:)\:} }}$

Where,

• s = semi - perimeter
• a = Length of side a
• b = Length of side b
• c = Length of side c

★ Solution:-    

~Semi - perimeter

$\qquad\sf{:\implies\:Semi\:-\:perimeter\:=\:\dfrac{a\:+\:b\:+c}{2}}$

$\qquad\sf{:\implies\:Semi\:-\:perimeter\:=\:\dfrac{325\:+\:300\:+125}{2}}$

$\qquad\sf{:\implies\:Semi\:-\:perimeter\:=\:\dfrac{750}{2}}$

$\qquad\sf{:\implies\:Semi\:-\:perimeter\:=\:375\:m}$

Hence the semi - perimeter is 375 m.

$\qquad\qquad\underline{\qquad\:\qquad\qquad\qquad}$

~Area of the triangular field

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{s\:(\:s\:-\:a\:)\:(\:s\:-\:b\:)\:(\:s\:-\:c\:)\:} }$

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{375\:(\:375\:-\:325\:)\:(\:375\:-\:300\:)\:(\:375\:-\:125\:)\:} }$

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{375\:(\:50\:)\:(\:75\:)\:(\:250\:)\:} }$

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{375\:\times\:50\:\times\:75\:\times\:250\:} }$

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{35,15,62,500} }$

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:18750\:m^{2}}$

Hence the area of the triangular field is 18750 m².