Question

Find the area of the triangle ABCD whose verticies are A(-5,7)B(-4,-5)C(4,5)​

Answer 1

SOLUTION :-

We know that,

$\bf Area \ of \ triangle = \dfrac{1}{2}\times [ \ x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2) \ ]$

Here,

$\bullet\sf \ x_1=-5 \ , \ y_1=7 \\\\\bullet \ x_2=-4 \ , \ y_2= -5 \\\\\bullet \ x_3= 4 \ , \ y_3 = 5$

Area of ΔABC :-

$\longrightarrow\sf \dfrac{1}{2} \times [ \ -5(-5-5)+-4(5-7)+4(7-(-5)) \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ -5(-5-5)+-4(5-7)+4(7+5) \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ (-5\times -10)+(-4 \times -2)+(4\times 12 ) \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ 50+8+48 \ ] \\\\\longrightarrow \dfrac{1}{2} \times 106 \\\\\longrightarrow 53 \ units$

Area of triangle ABC = 53 units