Question

Find the area of the triangle whose vertices are
(5,2)(3,-5) and (-5, -1)
​

Answer 1

★Answer :-

Consider any triangle with the given Coordinates

$\setlength{\unitlength}{1.6mm}\begin{picture}(30,20)\put(-3,-3){\line(1,1){12}}\put(-3,-3){\line(1,0){20}}\put(17,-3){\line(-2,3){8}}\end{picture}$

★ Concept Used :-

• We will use the formula of area of triangle. Here, the vertices are given in the question

$\sf{\ x_{1},\ y_{1}}$=(5,2)

$\sf{\ x_{2},\ y_{2}}$=(3,-5)

$\sf{\ x_{3},\ y_{3}}$=(-5,-1)

Formula :-

$\small\sf{\underline{\boxed{\purple{\dfrac{1}{2}[\ x_{1}(\ y_{2}-\ y_{3})+\ x_{2}(\ y_{3}-\ y_{1})+\ x_{3}(\ y_{1}-\ y_{2})]}}}}$

★Solution :-

$\small\sf{\dfrac{1}{2}[5(-5-(-1))+3(-1-2)+(-5)(2-(-5))]}$

$\small\sf{\dfrac{1}{2}[5(-5+1)+3(-1-2)-5(2+5)]}$

$\small\sf{\dfrac{1}{2}[5(-4)+3(-3)-5(7)]}$

$\small\sf{\dfrac{1}{2}[-20-9-35]}$

$\small\sf{\dfrac{1}{2}[-64]}$

$\sf{-32\:unit}$

But Area can't be negative

$\sf{\boxed{\boxed{\orange{\dag{Area=32\:sq.\:unit}}}}}$

So, the Area of the triangle is 32 sq. unit