Question

1. find an expression, in its simplest form, for the perimeter of this polygon.

Explanation:

Step1: Recall perimeter formula

The perimeter of a polygon is the sum of the lengths of its sides.

Step2: Identify side - lengths

The side - lengths of the polygon are \(x + 1\), \(2x+2\), \(x\), \(x\), \(2x + 1\).

Step3: Sum up the side - lengths

\((x + 1)+(2x + 2)+x+x+(2x + 1)\)

Step4: Combine like terms

\((x+2x+x+x+2x)+(1 + 2+1)=7x + 4\)

Answer:

\(7x + 4\)