I'm going to guess the question is determine the perimeter and area of a triangle SBA, S(15,-8), B(-2,21), A(0.0).
When we have a triangle with one vertex on the origin, the signed area is half the cross product of the other two vertices:
Area = (1/2) | 15(21) - (-8)(-2) | = (1/2)(299) = 149.5
It seems silly to round this exact answer, but we do what we're told.
Answer: Area=150
The perimeter P is the sum of the lengths of the three sides, so we use the distance formula three times. 8,15,17 is a known Pythagorean Triple.
[tex]P=\sqrt{(15 - -2)^2 + (-8 - 21)^2} + \sqrt{(-2)^2 + 21^2} + \sqrt{15^2 + (-8)^2}[/tex]
[tex]P = \sqrt{1130} + \sqrt{445} +17[/tex]
[tex]P \approx 71.71[/tex]
Answer: Perimeter=72
