## mayankdevnani Group Title 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) $712 cm^2$ one year ago one year ago

1. sauravshakya Group Title

Use herons formula to calculate the area of one half of the parallelogram.

2. sauravshakya Group Title

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3. sauravshakya Group Title

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4. mayankdevnani Group Title

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5. chihiroasleaf Group Title

yes.., s = 54, then what is the area of the triangle?

6. sauravshakya Group Title

Good going

7. mayankdevnani Group Title

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8. chihiroasleaf Group Title

yup..., now simplify ...

9. mayankdevnani Group Title

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10. mayankdevnani Group Title

now, then multiply it by 2 to get 612 cm^2. so option c is right answer.....right???

11. chihiroasleaf Group Title

right... :)

12. mayankdevnani Group Title

right? @chihiroasleaf and @sauravshakya

13. mayankdevnani Group Title

any short method!!!!

14. mayankdevnani Group Title

@hartnn @sirm3d @amistre64 @AravindG @AccessDenied any short method!!!to solve this question!!!

15. mayankdevnani Group Title

@DLS @satellite73 @nubeer plz help me!!!

16. DLS Group Title

if u were given the co-ordinates then I would've given u a shorter method

17. mayankdevnani Group Title

no, i am in 9 class its very long method

18. DLS Group Title

-_-

19. mayankdevnani Group Title

anyways!!! thnx...

20. scarydoor Group Title

I may have a way of calculating those coordinates quickly: |dw:1354889186448:dw| $x^2+y^2=c^2\\x^2+(y-a)^2=b^2\\x^2+y^2+a^2-2ay=b^2\\c^2+a^2-2ay=b^2\\y=\frac{b^2-c^2-a^2}{2a}\\x=\sqrt{\frac{b^2-a^2}{-2a}}$

21. scarydoor Group Title

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?

22. scarydoor Group Title
23. scarydoor Group Title

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.

24. mayankdevnani Group Title

thnx... @scarydoor

25. scarydoor Group Title

actually the formula for x might be slightly off.... but it can be fixed I think.