Question

Find the area of triangle whose side is 12cm,6cm,15cm by heron formula

Answer 1

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Answer 2

★ Required answer:-

                                                      

• Area of the triangular field is 34.19 cm².

                                   

★ Given:-    

                               

• ⇒ Length of side a = 12 cm
• ⇒ Length of side b = 6 cm
• ⇒ Length of side 15 cm

                               

★ To find:-    

                               

• Area of the triangle

                               

★ Formula used:-  

                               

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

Where,

• a = Length of side a = 12 cm
• b = Length of side b = 6 cm
• c = Length of side c = 15 cm

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

                                        

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

Where,

• S = semi - perimeter
• a = Length of side a = 12 cm
• b = Length of side b = 6 cm
• c = Length of side c = 15 cm

                                                        

★ Solution:-  

                                       

~Semi - perimeter

                          

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

                              

$\qquad\sf{:\implies\:Semi\:-\:perimeter\:=\:\left\{\:\dfrac{12\:+\:6\:+\:15}{2}\:\right\}}$

                         

$\qquad\sf{:\implies\:Semi\:-\:perimeter\:=\:\left\{\:\dfrac{33}{2}\:\right\}}$

                       

$\qquad\sf{:\implies\:Semi\:-\:perimeter\:=\:16.5}$

                                                                        

Hence the semi-perimeter is 16.5 cm

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

                                  

~Area of the triangle

                             

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

                              

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{16.5\:(\:16.5\:-\:12\:)\:(\:16.5\:-\:6\:)\:(\:16.5\:-\:15\:)} }$

                               

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{16.5\:(\:4.5\:)\:(\:10.5\:)\:(\:1.5\:)} }$

                           

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{16.5\:\times\:4.5\:\times\:10.5\:\times\:1.5\:} }$

                               

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{1169.4375} }$

                        

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:34.19\:cm^{2}}$

                                                                                         

Hence the area of the triangle is 34.19 cm²