The area of the triangle ABC with altitude CD is; 18.
What is the area of the triangle?
It follows from the task content that the length of the altitude can be evaluated as;
altitude = √((3-0)² +(-3-0)²)
altitude = 3√2.
Consequently, it follows that the base of the triangle is AB and its length is;
base = √((5-(-1))² + (-1-(-7))²)
base = 6√2.
Hence, the area of the triangle is;
Area = (1/2) × 3√2 × 6√2
Area = 18.
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