The problem asks us to find the perimeter of the given shape. The shape is a rectangle with a cutout on the bottom side. The dimensions are given in inches. The top side is 111 inches, the left side is 42 inches, the cutout depth is 18 inches, and the cutout width is 66 inches.

1. Problem Description

The problem asks us to find the perimeter of the given shape. The shape is a rectangle with a cutout on the bottom side. The dimensions are given in inches. The top side is 111 inches, the left side is 42 inches, the cutout depth is 18 inches, and the cutout width is 66 inches.

2. Solution Steps

The perimeter is the sum of all the sides of the shape.

* The top side is 111 inches.

* The left side is 42 inches.

* The right side is 42 inches.

* The bottom side has three segments.

* The middle segment is 66 inches.

* The remaining length on the left is $(111 - 66) / 2 = 45 / 2 = 22.5$ inches.

* The remaining length on the right is $(111 - 66) / 2 = 45 / 2 = 22.5$ inches.

* The length of the vertical segment on the left of the cutout is 18 inches.

* The length of the vertical segment on the right of the cutout is 18 inches.

The perimeter is the sum of the lengths of all the sides:

$P = 111 + 42 + 42 + 66 + 22.5 + 22.5 + 18 + 18$

$P = 111 + 84 + 66 + 45 + 36$

$P = 195 + 66 + 81$

$P = 261 + 81$

$P = 342$

Perimeter = $111 + 42 + 42 + (111 - 66) + 18 + 66 + 18 + (111 - 66)$

Perimeter = $111 + 42 + 42 + (45/2) + 18 + 66 + 18 + (45/2)$

Perimeter = $111 + 42 + 42 + 22.5 + 18 + 66 + 18 + 22.5$

Perimeter = $111 + 84 + 66 + 36 + 45$

Perimeter = $195 + 102 + 45$

Perimeter = $297 + 45$

Perimeter = $342$

3. Final Answer

342 in