## mayankdevnani 2 years ago 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) $712 cm^2$

1. sauravshakya

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

2. sauravshakya

|dw:1354886905111:dw|

3. sauravshakya

|dw:1354886978203:dw|

4. mayankdevnani

|dw:1354887034102:dw|

5. chihiroasleaf

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

6. sauravshakya

Good going

7. mayankdevnani

|dw:1354887176565:dw|

8. chihiroasleaf

yup..., now simplify ...

9. mayankdevnani

|dw:1354887394948:dw|

10. mayankdevnani

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

11. chihiroasleaf

right... :)

12. mayankdevnani

right? @chihiroasleaf and @sauravshakya

13. mayankdevnani

any short method!!!!

14. mayankdevnani

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

15. mayankdevnani

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

16. DLS

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

17. mayankdevnani

no, i am in 9 class its very long method

18. DLS

-_-

19. mayankdevnani

anyways!!! thnx...

20. scarydoor

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

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
23. scarydoor

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

thnx... @scarydoor

25. scarydoor

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