Question

what is the perimeter of the parallelogram?
units
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Explanation:

Step1: Identify base length

The base of the parallelogram spans 5 grid units, so base $b = 5$.

Step2: Calculate slant side length

The slant side forms a right triangle with horizontal 3 units, vertical 8 units. Use Pythagorean theorem:
$$s = \sqrt{3^2 + 8^2} = \sqrt{9 + 64} = \sqrt{73}$$

Step3: Compute perimeter

Perimeter of parallelogram: $2(b + s)$
$$2(5 + \sqrt{73}) = 10 + 2\sqrt{73}$$
Or approximate: $2\sqrt{73} \approx 17.09$, so $10 + 17.09 = 27.09$

Answer:

$10 + 2\sqrt{73}$ (or approximately 27.1 units)