The area of the triangle CDE is 8 square units
How to determine the triangle area?
The coordinates of the triangle CDE are given as:
C(3,-2), D(-1, 2), E(2, 3)
The altitude is given as: EF
Where F = (0,1)
Calculate the length EF using:
[tex]EF = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
This gives
[tex]EF = \sqrt{(2 -0)^2 + (3 -1)^2} = \sqrt{8}[/tex]
Calculate the base length CD using
[tex]CD = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
This gives
[tex]CD = \sqrt{(3 +1)^2 + (-2 -2)^2} = \sqrt{32[/tex]
The area is then calculated using:
Area = 0.5 * EF * CD
So, we have:
Area = 0.5 * √32 * √8
Evaluate
Area = 8
Hence, the area of the triangle CDE is 8 square units
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