The formula to calculate the Short Diagonal of Parallelogram (dShort) is:
\[ dShort = \sqrt{(2 \times eLong^2) + (2 \times eShort^2) - dLong^2} \]
Where:
Short Diagonal of Parallelogram is the length of the line joining the pair of obtuse angle corners of a Parallelogram.
Long Edge of Parallelogram is the length of the longest pair of parallel sides in a Parallelogram.
Short Edge of Parallelogram is the length of the shortest pair of parallel edges in a Parallelogram.
Long Diagonal of Parallelogram is the length of the line joining the pair of acute angle corners of a Parallelogram.
Let's assume the following values:
Using the formula:
\[ dShort = \sqrt{(2 \times eLong^2) + (2 \times eShort^2) - dLong^2} \]
Evaluating:
\[ dShort = \sqrt{(2 \times 12^2) + (2 \times 7^2) - 18^2} \]
The Short Diagonal of Parallelogram is 7.87400787401181 meters.
| Long Edge of Parallelogram (meters) | Short Edge of Parallelogram (meters) | Long Diagonal of Parallelogram (meters) | Short Diagonal of Parallelogram (meters) |
|---|---|---|---|
| 10 | 5 | 15 | 5.000000000000000 |
| 10 | 5 | 16 | nan |
| 10 | 5 | 17 | nan |
| 10 | 5 | 18 | nan |
| 10 | 5 | 19 | nan |
| 10 | 5 | 20 | nan |
| 10 | 6 | 15 | 6.855654600401044 |
| 10 | 6 | 16 | 4.000000000000000 |
| 10 | 6 | 17 | nan |
| 10 | 6 | 18 | nan |
| 10 | 6 | 19 | nan |
| 10 | 6 | 20 | nan |
| 10 | 7 | 15 | 8.544003745317530 |
| 10 | 7 | 16 | 6.480740698407860 |
| 10 | 7 | 17 | 3.000000000000000 |
| 10 | 7 | 18 | nan |
| 10 | 7 | 19 | nan |
| 10 | 7 | 20 | nan |
| 10 | 8 | 15 | 10.148891565092219 |
| 10 | 8 | 16 | 8.485281374238570 |
| 10 | 8 | 17 | 6.244997998398398 |
| 10 | 8 | 18 | 2.000000000000000 |
| 10 | 8 | 19 | nan |
| 10 | 8 | 20 | nan |
| 10 | 9 | 15 | 11.704699910719626 |
| 10 | 9 | 16 | 10.295630140987001 |
| 10 | 9 | 17 | 8.544003745317530 |
| 10 | 9 | 18 | 6.164414002968976 |
| 10 | 9 | 19 | 1.000000000000000 |
| 10 | 9 | 20 | nan |
| 10 | 10 | 15 | 13.228756555322953 |
| 10 | 10 | 16 | 12.000000000000000 |
| 10 | 10 | 17 | 10.535653752852738 |
| 10 | 10 | 18 | 8.717797887081348 |
| 10 | 10 | 19 | 6.244997998398398 |
| 10 | 10 | 20 | 0.000000000000000 |
| 11 | 5 | 15 | 8.185352771872450 |
| 11 | 5 | 16 | 6.000000000000000 |
| 11 | 5 | 17 | 1.732050807568877 |
| 11 | 5 | 18 | nan |
| 11 | 5 | 19 | nan |
| 11 | 5 | 20 | nan |
| 11 | 6 | 15 | 9.433981132056603 |
| 11 | 6 | 16 | 7.615773105863909 |
| 11 | 6 | 17 | 5.000000000000000 |
| 11 | 6 | 18 | nan |
| 11 | 6 | 19 | nan |
| 11 | 6 | 20 | nan |
| 11 | 7 | 15 | 10.723805294763608 |
| 11 | 7 | 16 | 9.165151389911680 |
| 11 | 7 | 17 | 7.141428428542850 |
| 11 | 7 | 18 | 4.000000000000000 |
| 11 | 7 | 19 | nan |
| 11 | 7 | 20 | nan |
| 11 | 8 | 15 | 12.041594578792296 |
| 11 | 8 | 16 | 10.677078252031311 |
| 11 | 8 | 17 | 9.000000000000000 |
| 11 | 8 | 18 | 6.782329983125268 |
| 11 | 8 | 19 | 3.000000000000000 |
| 11 | 8 | 20 | nan |
| 11 | 9 | 15 | 13.379088160259652 |
| 11 | 9 | 16 | 12.165525060596439 |
| 11 | 9 | 17 | 10.723805294763608 |
| 11 | 9 | 18 | 8.944271909999159 |
| 11 | 9 | 19 | 6.557438524302000 |
| 11 | 9 | 20 | 2.000000000000000 |
| 11 | 10 | 15 | 14.730919862656235 |
| 11 | 10 | 16 | 13.638181696985855 |
| 11 | 10 | 17 | 12.369316876852981 |
| 11 | 10 | 18 | 10.862780491200215 |
| 11 | 10 | 19 | 9.000000000000000 |
| 11 | 10 | 20 | 6.480740698407860 |
| 12 | 5 | 15 | 10.630145812734650 |
| 12 | 5 | 16 | 9.055385138137417 |
| 12 | 5 | 17 | 7.000000000000000 |
| 12 | 5 | 18 | 3.741657386773941 |
| 12 | 5 | 19 | nan |
| 12 | 5 | 20 | nan |
| 12 | 6 | 15 | 11.618950038622250 |
| 12 | 6 | 16 | 10.198039027185569 |
| 12 | 6 | 17 | 8.426149773176359 |
| 12 | 6 | 18 | 6.000000000000000 |
| 12 | 6 | 19 | nan |
| 12 | 6 | 20 | nan |
| 12 | 7 | 15 | 12.688577540449520 |
| 12 | 7 | 16 | 11.401754250991379 |
| 12 | 7 | 17 | 9.848857801796104 |
| 12 | 7 | 18 | 7.874007874011811 |
| 12 | 7 | 19 | 5.000000000000000 |
| 12 | 7 | 20 | nan |
| 12 | 8 | 15 | 13.820274961085254 |
| 12 | 8 | 16 | 12.649110640673518 |
| 12 | 8 | 17 | 11.269427669584644 |
| 12 | 8 | 18 | 9.591663046625438 |
| 12 | 8 | 19 | 7.416198487095663 |
| 12 | 8 | 20 | 4.000000000000000 |
| 12 | 9 | 15 | 15.000000000000000 |
| 12 | 9 | 16 | 13.928388277184119 |
| 12 | 9 | 17 | 12.688577540449520 |
| 12 | 9 | 18 | 11.224972160321824 |
| 12 | 9 | 19 | 9.433981132056603 |
| 12 | 9 | 20 | 7.071067811865476 |
| 12 | 10 | 15 | 16.217274740226856 |
| 12 | 10 | 16 | 15.231546211727817 |
| 12 | 10 | 17 | 14.106735979665885 |
| 12 | 10 | 18 | 12.806248474865697 |
| 12 | 10 | 19 | 11.269427669584644 |
| 12 | 10 | 20 | 9.380831519646859 |
| 13 | 5 | 15 | 12.767145334803704 |
| 13 | 5 | 16 | 11.489125293076057 |
| 13 | 5 | 17 | 9.949874371066199 |
| 13 | 5 | 18 | 8.000000000000000 |
| 13 | 5 | 19 | 5.196152422706632 |
| 13 | 5 | 20 | nan |
| 13 | 6 | 15 | 13.601470508735444 |
| 13 | 6 | 16 | 12.409673645990857 |
| 13 | 6 | 17 | 11.000000000000000 |
| 13 | 6 | 18 | 9.273618495495704 |
| 13 | 6 | 19 | 7.000000000000000 |
| 13 | 6 | 20 | 3.162277660168380 |
| 13 | 7 | 15 | 14.525839046333950 |
| 13 | 7 | 16 | 13.416407864998739 |
| 13 | 7 | 17 | 12.124355652982141 |
| 13 | 7 | 18 | 10.583005244258363 |
| 13 | 7 | 19 | 8.660254037844387 |
| 13 | 7 | 20 | 6.000000000000000 |
| 13 | 8 | 15 | 15.524174696260024 |
| 13 | 8 | 16 | 14.491376746189438 |
| 13 | 8 | 17 | 13.304134695650070 |
| 13 | 8 | 18 | 11.916375287812984 |
| 13 | 8 | 19 | 10.246950765959598 |
| 13 | 8 | 20 | 8.124038404635961 |
| 13 | 9 | 15 | 16.583123951777001 |
| 13 | 9 | 16 | 15.620499351813308 |
| 13 | 9 | 17 | 14.525839046333950 |
| 13 | 9 | 18 | 13.266499161421599 |
| 13 | 9 | 19 | 11.789826122551595 |
| 13 | 9 | 20 | 10.000000000000000 |
| 13 | 10 | 15 | 17.691806012954132 |
| 13 | 10 | 16 | 16.792855623746664 |
| 13 | 10 | 17 | 15.779733838059499 |
| 13 | 10 | 18 | 14.628738838327793 |
| 13 | 10 | 19 | 13.304134695650070 |
| 13 | 10 | 20 | 11.747340124470730 |
| 14 | 5 | 15 | 14.730919862656235 |
| 14 | 5 | 16 | 13.638181696985855 |
| 14 | 5 | 17 | 12.369316876852981 |
| 14 | 5 | 18 | 10.862780491200215 |
| 14 | 5 | 19 | 9.000000000000000 |
| 14 | 5 | 20 | 6.480740698407860 |
| 14 | 6 | 15 | 15.459624833740307 |
| 14 | 6 | 16 | 14.422205101855956 |
| 14 | 6 | 17 | 13.228756555322953 |
| 14 | 6 | 18 | 11.832159566199232 |
| 14 | 6 | 19 | 10.148891565092219 |
| 14 | 6 | 20 | 8.000000000000000 |
| 14 | 7 | 15 | 16.278820596099706 |
| 14 | 7 | 16 | 15.297058540778355 |
| 14 | 7 | 17 | 14.177446878757825 |
| 14 | 7 | 18 | 12.884098726725126 |
| 14 | 7 | 19 | 11.357816691600547 |
| 14 | 7 | 20 | 9.486832980505138 |
| 14 | 8 | 15 | 17.175564037317667 |
| 14 | 8 | 16 | 16.248076809271922 |
| 14 | 8 | 17 | 15.198684153570664 |
| 14 | 8 | 18 | 14.000000000000000 |
| 14 | 8 | 19 | 12.609520212918492 |
| 14 | 8 | 20 | 10.954451150103322 |
| 14 | 9 | 15 | 18.138357147217054 |
| 14 | 9 | 16 | 17.262676501632068 |
| 14 | 9 | 17 | 16.278820596099706 |
| 14 | 9 | 18 | 15.165750888103101 |
| 14 | 9 | 19 | 13.892443989449804 |
| 14 | 9 | 20 | 12.409673645990857 |
| 14 | 10 | 15 | 19.157244060668017 |
| 14 | 10 | 16 | 18.330302779823359 |
| 14 | 10 | 17 | 17.406895185529212 |
| 14 | 10 | 18 | 16.370705543744901 |
| 14 | 10 | 19 | 15.198684153570664 |
| 14 | 10 | 20 | 13.856406460551018 |
| 15 | 5 | 15 | 16.583123951777001 |
| 15 | 5 | 16 | 15.620499351813308 |
| 15 | 5 | 17 | 14.525839046333950 |
| 15 | 5 | 18 | 13.266499161421599 |
| 15 | 5 | 19 | 11.789826122551595 |
| 15 | 5 | 20 | 10.000000000000000 |
| 15 | 6 | 15 | 17.233687939614086 |
| 15 | 6 | 16 | 16.309506430300090 |
| 15 | 6 | 17 | 15.264337522473747 |
| 15 | 6 | 18 | 14.071247279470288 |
| 15 | 6 | 19 | 12.688577540449520 |
| 15 | 6 | 20 | 11.045361017187261 |
| 15 | 7 | 15 | 17.972200755611428 |
| 15 | 7 | 16 | 17.088007490635061 |
| 15 | 7 | 17 | 16.093476939431081 |
| 15 | 7 | 18 | 14.966629547095765 |
| 15 | 7 | 19 | 13.674794331177344 |
| 15 | 7 | 20 | 12.165525060596439 |
| 15 | 8 | 15 | 18.788294228055936 |
| 15 | 8 | 16 | 17.944358444926362 |
| 15 | 8 | 17 | 17.000000000000000 |
| 15 | 8 | 18 | 15.937377450509228 |
| 15 | 8 | 19 | 14.730919862656235 |
| 15 | 8 | 20 | 13.341664064126334 |
| 15 | 9 | 15 | 19.672315572906001 |
| 15 | 9 | 16 | 18.867962264113206 |
| 15 | 9 | 17 | 17.972200755611428 |
| 15 | 9 | 18 | 16.970562748477139 |
| 15 | 9 | 19 | 15.842979517754859 |
| 15 | 9 | 20 | 14.560219778561036 |
| 15 | 10 | 15 | 20.615528128088304 |
| 15 | 10 | 16 | 19.849433241279208 |
| 15 | 10 | 17 | 19.000000000000000 |
| 15 | 10 | 18 | 18.055470085267789 |
| 15 | 10 | 19 | 17.000000000000000 |
| 15 | 10 | 20 | 15.811388300841896 |