Area of the polygon defined by the given points is 62.5 sq units
Step-by-step explanation:
Step 1 :
Let P be the point (-5,0) Q = (0,-5), R = (-15,-20) and S = (20,-15)
We have to to find the area of the polygon PQRS
Step 2 :
The area of polygon given the vertices (x[tex](x_{1} ,y_{1} ), (x_{2} ,y_{2}) ... (x_{n} ,y_{n} )[/tex] is given by
Area = mod ( [tex](x_{1} y_{2} - y_{1}x_{2}) + (x_{2} y_{3} - y_{2}x_{3}) + ... (x_{n} y_{1} - y_{n}x_{1})[/tex] ) ÷ 2
Where [tex]x_{n}[/tex] is the vertex n's x coordinate , [tex]y_{n}[/tex] is the vertex n's y coordinate
Substituting the corresponding values ,
Area of PQRS = mod ( (25 - 0)+ (0-75) +(300-300) +( 0-75) ) ÷ 2
= mod (25-75+0-75) ÷ 2
= mod (-125) ÷ 2 = 125 ÷ 2 = 62.5 sq units
Step 3 :
Answer :
Area of the polygon defined by the given points is 62.5 sq units
