Hey there!!
Basic formula :
√( x₂ - x₁ )² + (y₂ - y₁ )²
Coordinates :
R ( -1 , 3 ) ; S ( 3 , 3 ) ; T ( 5 , -1 ) ; U ( -2 , -1 )
Let us see the distance of the segment of RS
( x₂ = 3 , x₁ = -1 ) ( y₂ = 3 , x₁ = 3 )
√ ( 3 - ( -1 ) )² + ( 3 - 3 )²
√ ( 3 + 1 )² + ( 0 )²
√ ( 4 )² + 0
√ 16
= 4
First side = 4
Now, let us find the ST
( 3 , 3 ) ( 5 , - 1 )
( x₂ = 5 , x₁ = 3 ) ; ( y₂ = -1 , y₁ = 3 )
√ ( 5 - 3 )² + ( -1 - 3 )²
√ ( 2 )² + ( -4 )²
√ 4 + 16
√20
√4 × √5
the length of this side = 2√5 = 4.47
The length of TU :
( 5 , -1 ) ( -2 , -1 )
( x₂ = -2 , x₁ = 5 ) ; ( y₂ = -1 , y₁ = -1 )
√ ( -2 -5 )² + ( -1 + 1 )²
√ ( -7 )² + ( 0 )²
√ 49 = 7
The length of the third side = 7
The length of RU :
( -1 , 3 ) ( -2 , -1 )
( x₂ = -2 , x₁ = -1 ) ; ( y₂ = -1 , y₁ = 3 )
√ ( -2 + 1 )² + ( -1-4 )²
√ ( - 1 )² + ( -5 )²
√ 1 + 25
√26 = 5.09
The length of the fourth side = 5.09
Perimeter = 4 + 4.47 + 7 + 5.09
= 20.56
The perimeter = 20.56
Rounded off = 21 0r 20.6
Hope my answer helps!