Two adjacent sides of a parallelogram are 51 cm and 37 cm. One of its diagonals is 20 cm, then its area is..... a) \[412 cm^2\] b) \[512 cm^2\] c) \[612 cm^2\] d) \[712 cm^2\]

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Two adjacent sides of a parallelogram are 51 cm and 37 cm. One of its diagonals is 20 cm, then its area is..... a) \[412 cm^2\] b) \[512 cm^2\] c) \[612 cm^2\] d) \[712 cm^2\]

Mathematics
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Use herons formula to calculate the area of one half of the parallelogram.
|dw:1354886905111:dw|
|dw:1354886978203:dw|

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Other answers:

|dw:1354887034102:dw|
yes.., s = 54, then what is the area of the triangle?
Good going
|dw:1354887176565:dw|
yup..., now simplify ...
|dw:1354887394948:dw|
now, then multiply it by 2 to get 612 cm^2. so option c is right answer.....right???
right... :)
any short method!!!!
@hartnn @sirm3d @amistre64 @AravindG @AccessDenied any short method!!!to solve this question!!!
@DLS @satellite73 @nubeer plz help me!!!
  • DLS
if u were given the co-ordinates then I would've given u a shorter method
no, i am in 9 class its very long method
  • DLS
-_-
anyways!!! thnx...
I may have a way of calculating those coordinates quickly: |dw:1354889186448:dw| \[x^2+y^2=c^2\\x^2+(y-a)^2=b^2\\x^2+y^2+a^2-2ay=b^2\\c^2+a^2-2ay=b^2\\y=\frac{b^2-c^2-a^2}{2a}\\x=\sqrt{\frac{b^2-a^2}{-2a}}\]
So now you know the coordinates of the parallelogram. There is a formula from algebra about how to calculate the area. It involves cross products or inner products or something?
http://en.wikipedia.org/wiki/Parallelogram#The_area_on_coordinate_system
If you had good memory, you could just memorise the formula for x and y that I derived above. (I think it's right...) Then calculating the area would take about three lines.
thnx... @scarydoor
actually the formula for x might be slightly off.... but it can be fixed I think.

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