Question

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

Show ALL your work! Your choice of method on how to find the area.

Answer 1

Area of the triangle is 10 sq.units

Solution-

We know that,

`\text{Area of the triangle}=(1)/(2)[{x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]`

Taking,

(x₁, y₁) = (3, 3)

(x₂, y₂) = (3, -1)

(x₃, y₃) = (-2, -5)

Then putting these in the formula,

`\text{Area of the triangle}=(1)/(2)[3(-1+5)+3(-5-3)-2(3+1)]`

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

`=(1)/(2)[12-24-8]`

`=(1)/(2)[-20]`

`=-10`

As area can not be negative, ignoring negative sign,

`\text{Area of the triangle}=10`