Quote:
In parallelogram ABCD below, ﬁnd the following.
(a) Area of ABCD
(b) Perimeter of ABCD
(c) Length of diagonal BD
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.
_________________