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# In parallelogram ABCD below, ﬁnd the following. (a) Area of

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In parallelogram ABCD below, ﬁnd the following. (a) Area of [#permalink]  26 May 2019, 03:21
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In parallelogram ABCD below, ﬁnd the following.

(a) Area of ABCD

(b) Perimeter of ABCD

(c) Length of diagonal BD

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#GREexacercise In parallelogram ABCD below, ﬁnd the following.jpg [ 14.9 KiB | Viewed 10115 times ]

[Reveal] Spoiler: OA
(a) 48 (b) $$24 + 4 \sqrt{5}$$ (c) $$2 \sqrt{29}$$

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Re: In parallelogram ABCD below, ﬁnd the following. (a) Area of [#permalink]  26 May 2019, 08:29
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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.
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Re: In parallelogram ABCD below, ﬁnd the following. (a) Area of   [#permalink] 26 May 2019, 08:29
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