Area of triangle is the half of the product of its base and height. The area of the given triangle is 144 squared unit.
Given information-
The coordinates of the point D is (-8,8).
The coordinates of the point E is (10,-2).
The coordinates of the point F is (-8,-8).
Area of triangle-
Area of triangle is the half of the product of its base and height.
The length of the DF is the base of the triangle. The distance of the base DF is,
[tex]DF=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\
DF=\sqrt{(-8-(-8))^2+(-8-8)^2} \\
DF=\sqrt{(0)^2+(-16)^2} \\
DF=\sqrt{256} \\
DF=16[/tex]
Thus the length of the base DF is 16 units.
Drop a perpendicular O from point E to the line DF. The coordinates of O are (-8,-2).
The length of the OE is the height of the triangle. The distance of the height OE is,
[tex]OE=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\
OE=\sqrt{(-8-10)^2+(-2-(-2))^2} \\
OE=\sqrt{(-18)^2+0} \\
OE=\sqrt{324} \\
DE=18[/tex]
Thus the height of the triangle is 18 units.
Thus the area of the triangle is,
[tex]A=\dfrac{1}{2} \times DF\times OE\\
A=\dfrac{1}{2} \times 16\times 18\\
A=144[/tex]
Thus the area of the given triangle is 144 squared unit.
Learn more about the area of the triangle here;
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