Question

Find the area of the polygon defined by the coordinates (0,-5),(-5,0),(-15,-20),and(-20,-15)

Answer 1

Area of the polygon defined by the given points is 62.5 sq units

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
`(x_(1) ,y_(1) ), (x_(2) ,y_(2)) ... (x_(n) ,y_(n) )` is given by

Area = mod (
`(x_(1) y_(2) - y_(1)x_(2)) + (x_(2) y_(3) - y_(2)x_(3)) + ... (x_(n) y_(1) - y_(n)x_(1))` ) ÷ 2

Where
`x_(n)` is the vertex n's x coordinate ,
`y_(n)` 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