Find the area (in cm^2) of a parallelogram whose adjacent sides are 14 cm and 10 cm and the angle between these sides is 30.
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The sides of a parallelogram are 6cm and 14cm and an angle between them is 30, what are the length of its diagonals?
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2 ANSWERS

Girija Warrier, Passionate about Maths & Music...
Answered Oct 22, 2017 · Author has 2.2kanswers and 2.2m answer views
Diagonals can be calculated by cosine law..
If diagonal opposite to 30° = d1
Then, by cosine law…
d1² = 14² + 6² - 2*14*6 * cos30°
=> d1² = 196 + 36 - 168 * √3/2
=> d1² = 232 - 168* 0.865
=> d1² = 232 - 145.68
=> d1² = √86.68
=> d1 = 9.3 ( approx) ……………..(1)
Now, angle adjacent to 30° in parallelogram = (180- 30) = 150°
So, again by cosine law..
If diagonal opposite to 150° = d2
d2² = 14² + 6² - 2*14*6 *cos 150°
=> d2² = 196 + 36 - 168* cos(90°+60°)
=> d2² = 232 - 168 *( - sin60° )
=> d2² = 232 - 168 * (-√3/2)
=> d2² = 232 - 168 * - 0.86
=> d2² = 232 + 144.48
=> d2² = 376.48
=> d2 = √376.48
=> d2 = 19.4 ( approx) ……………….(2)
So, smaller diagonal = 9.3 cm ( approx)
& greater diagonal = 19.4 cm ( approx)
hope you have understanding
please make me happy
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2 ANSWERS

Girija Warrier, Passionate about Maths & Music...
Answered Oct 22, 2017 · Author has 2.2kanswers and 2.2m answer views
Diagonals can be calculated by cosine law..
If diagonal opposite to 30° = d1
Then, by cosine law…
d1² = 14² + 6² - 2*14*6 * cos30°
=> d1² = 196 + 36 - 168 * √3/2
=> d1² = 232 - 168* 0.865
=> d1² = 232 - 145.68
=> d1² = √86.68
=> d1 = 9.3 ( approx) ……………..(1)
Now, angle adjacent to 30° in parallelogram = (180- 30) = 150°
So, again by cosine law..
If diagonal opposite to 150° = d2
d2² = 14² + 6² - 2*14*6 *cos 150°
=> d2² = 196 + 36 - 168* cos(90°+60°)
=> d2² = 232 - 168 *( - sin60° )
=> d2² = 232 - 168 * (-√3/2)
=> d2² = 232 - 168 * - 0.86
=> d2² = 232 + 144.48
=> d2² = 376.48
=> d2 = √376.48
=> d2 = 19.4 ( approx) ……………….(2)
So, smaller diagonal = 9.3 cm ( approx)
& greater diagonal = 19.4 cm ( approx)
hope you have understanding
please make me happy
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Find area of parallelogram whose adjacent sides are 10cm and 12 cm with diagonal 14cm...
.......This is the question which they gave in my notebook.......
This is pretty easy.I hope you have some idea bout HERON'S FORMULA. Given 3 sides of a triangle, the area will be
A= √(s)(s-a)(s-b)(s-c)
Where s is semi(half) the perimeter.
Here we have s=a+b+c/2 =18cm.
Put back in the formula
√18(18-14)(18-12)(18-10)
=√18*4*6*8
=24√6 cm^2.
This is half the area of the parallelogram.
A*2 will give full area.
Thus answer is 48√6 cm^2.
To have a better understanding, here's the supplement question you can try.
A parallelogram has sides 30m and 14m and one of its diagonals is 40m long. Then its area is?
Cheers. Mark brainliest.
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