Question

What is a simplified expression for the perimeter of the polygon?

Answer 1

Answer:

D. 5x^2 + 2y^2 + 12x + 5y

Step-by-step explanation:

6x + 2y + y^2 + 6x + 2y + y^2 + 4x^2 + x^2 + y

6x + 6x = 12x

12x + 2y + y^2 + 2y  + y^2 + 4x^2 + x^2 + y

2y + 2y + y = 5y

12x + 5y + y^2 + y^2 + 4x^2 + x^2

y^2 + y^2 = 2y^2

2y^2 + 4x^2 + x^2 + 12x + 5y

4x^2 + x^2 = 5x^2

2y^2 + 5x^2  + 12x + 5y

5x^2 + 2y^2 + 12x + 5y

Answer 2

Answer:

$5 {x}^{2} + 2 {y}^{2} + 12x + 5y$

Step-by-step explanation:

Add all of the sides of the polygon:

$6x + 2y + {y}^{2} + 6x + 2y + {y}^{2} + 4 {x}^{2} + {x}^{2} + y$

Combine like terms.

$12x + 5y + 2 {y}^{2} + 5 {x}^{2}$

$5 {x}^{2} + 2 {y}^{2} + 12x + 5y$