Area of a parallelogram = base x height (where base is perpendicular to height)

Here base = 12, height = 4. Therefore area ABCD = 12 x 4 = 48.

Perimeter of a parallelogram = 2(length + width). Length AD is already provided as 12, so find the width CD using the Pythagorean Theorem a² + b² = c².

2² + 4² = 20. √20 and simplify to find that CD = 2√5. Therefore, the perimeter = 24 + 4√5.

Finally, imagine a line directly vertical from point D which would be equal to the vertical line down from Point C = 4.

Then, recognize that the length of the created right triangle would be 12-2 - 10.

Now, use the Pythagorean Theorem to find diagonal BD. 4² + 10² = 116. √116 and simplify to find that diagonal BD = 2√29.
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