Question

$\maltese$ QUESTION :-

The area of a triangle whose sides are 8 cm,42 cm and 44 cm, is


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Answer 1

★ Assumption Needed:-    

Let the sides be,

• ➾  Side a = 8 cm
• ➾  Side b = 42 cm
• ➾  Side c = 44 cm

★ To Calculate:-    

• ➾  Area of the triangle

★ Formula Used:-      

~Semi-Perimeter

• $\Large\boxed{\sf{Semi\:-\:Perimeter\:=\:\left(\dfrac{a\:+\:b\:+\:c}{2}\right)}}$

Where,

• ➾  a = 8 cm = Length of side a
• ➾  b = 42 cm = Length of side b
• ➾  c = 44 cm = Length of side c

~Area of the triangle

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

‏‏‎ ‎

Where,

• ➾  s = semi-perimeter
• ➾  a = 8 cm = Length of side a
• ➾  b = 42 cm = Length of side b
• ➾  c = 44 cm = Length of side c

★ Calculating:-      

Step1: First we need to find the semi-perimeter so we will substitute the values in the formula. [ Semi-perimeter = a + b + c/2 ]

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

$\qquad\sf{:\implies\:Semi\:-\:Perimeter\:=\:\left(\dfrac{8\:+\:42\:+\:44}{2}\right)}$

$\qquad\sf{:\implies\:Semi\:-\:Perimeter\:=\:\left(\dfrac{50\:+\:44}{2}\right)}$

$\qquad\sf{:\implies\:Semi\:-\:Perimeter\:=\:\left(\dfrac{94}{2}\right)}$

$\qquad\sf{:\implies\:Semi\:-\:Perimeter\:=\:47\:cm}$

$\therefore\underline{\sf{The\:Semi\:-\:Perimeter\:is\:47\:cm\:.}}$

Step2: Now to calculate the triangle area, we will again use the formula and substitute the values. [ Area of triangle = √s ( s - a ) ( s -b ) ( s - c )]

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

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{47\:(\:47\:-\:8\:)\:(\:47\:-\:42\:)\:(\:47\:-\:44\:)} }$

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{47\:(\:39\:)\:(\:5\:)\:(\:3\:)} }$

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{47\:\times\:39\:\times\:5\:\times\:3\:} }$

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\sqrt{27495} }$

$\qquad\sf{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:3\sqrt{3055} }$

$\therefore\underline{\sf{The\:Area\:of\:the\:triangle\:is\:3\sqrt{3055} \:cm^{2}\:.}}$

★ Answer:-      

• The area of the triangle is 3√3055 cm².