Question

Find the area of a triangle ABC whose vertices are a - 5 - 1 b 3 - 5 and C 5 and 2.​

Answer 1

Area of triangle is 32 square units.  

Given

To find the area of a triangle for the given vertices.  

Given vertices : ( - 5, - 1 ), ( 3, - 5 ), ( 5, 2 )

Formula :

Area of triangle =  $\frac{1}{2}$ × $[ x_{1} .(y_{2} - y_3) + x_{2} }.( y_{3} - y_{1}) + x_{3}.(y _{1} - y_{2}) ]$

                          = $\frac{1}{2}$ × $[ (-5).(-5-2) + (3).(2-(-1)) + (5).(-1-(-5)) ]$

                          = $\frac{1}{2}$ × $[ (-5).(-7) +(3).(2+1) + (5).(-1+5) ]$

                          = $\frac{1}{2}$ × $[ (35) + (3).(3) + (5).(4) ]$

                          = $\frac{1}{2}$ × $[ 35+9+20 ]$

                          = $\frac{1}{2}$ × $[ 64 ]$    

                          = 32 square units

Therefore, area of triangle is 32 square units.

To learn more...

1. brainly.in/question/7285493

2. brainly.in/question/8993582