Question

what is the perimeter of this shape?

Explanation:

Step1: Calculate outer rectangle perimeter

First, find the outer bounds: x ranges from -4 to 4 (length = $4 - (-4) = 8$), y ranges from -4 to 4 (width = $4 - (-4) = 8$). Perimeter of outer rectangle:
$2\times(8 + 8) = 32$

Step2: Add inner protruding segments

Each indent adds 2 segments of length 2 (top left, top right, bottom left, bottom right: 4 indents total, each contributes $2\times2$).
Total added length: $4\times(2\times2) = 16$

Step3: Sum total perimeter

Add outer perimeter and inner segments:
$32 + 16 = 48$

Answer:

48