Question

HELP PLEASE!

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

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__units²

Answer 1

Find out the Area of a triangle .

To proof

Formula

Area of Triangle

`= (1)/(2)*( {x_1(y_(2)-y_(3)) +x_(2)(y_(3) - y_(1))+x_(3)(y_(1)-y_(2))})`

Now vertices are D(3, 3) , E(3, −1) , and F(−2, −5) .

`= (1)/(2) (3*(-1 +5) + 3*(-5-3)-2*(3+1))`

Solving the above

`= (1)/(2)(3*4+3*-8 -2*4)`

`=(1)/(2) (12-24-8)\\ =(1)/(2) (-32+12)\\=(1)/(2) (-20)`

= -10 units²

(Neglected the negative sign as area cannot be negative.)

= 10 units ²

Area of a triangle is 10 units ²

Hence proved