Question

What is the area of a triangle whose vertices are D(3, 3) , E(3, −1) , and F(−2, −5) ?

Answer 1

The points given are: $D=(3,3),E=(3,-1),F=(-2-5)$

Area of the triangle is given by:

$A = \frac{1}{2}| ( x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) )|$

$A = \frac{1}{2} |(3(-1+5) + 3(-5-3) -2(3+1))|$

$A = \frac{1}{2}|(3(4) + 3(-8) -2(4))|$

$A = \frac{1}{2} |( 12 -24 -8))|$

$A = \frac{1}{2} |( -20)|$

$A = |-10|$

$A = 10 \ units^2$