Follow a worked example.
Every example below can be loaded using its calculator’s Reset example button. Inputs use centimetres, square centimetres or cubic centimetres as labelled, while angles use degrees.
Perpendicular diagonals
Given: Symmetry diagonal p = 10; Crossing diagonal q = 6.
A = pq/2
| Measurement | Calculated value |
|---|---|
| Area | 30 cm² |
Adjacent side lengths and crossing diagonal
Given: Side pair a = 5; Side pair b = 7; Crossing diagonal d = 6.
p = √(a²−d²/4) + √(b²−d²/4)
| Measurement | Calculated value |
|---|---|
| Area | 30.973666 cm² |
| Perimeter | 24 cm |
| Symmetry diagonal | 10.324555 cm |
| Crossing diagonal | 6 cm |
Area to missing diagonal
Given: Area A = 30; Known diagonal p = 10.
q = 2A/p
| Measurement | Calculated value |
|---|---|
| Missing perpendicular diagonal | 6 cm |
Symmetry diagonal segments and crossing diagonal
Given: Upper segment p = 4; Lower segment q = 6; Crossing diagonal d = 6.
a = √(p²+d²/4); b = √(q²+d²/4)
| Measurement | Calculated value |
|---|---|
| Area | 30 cm² |
| Perimeter | 23.416408 cm |
| Symmetry diagonal | 10 cm |
| Crossing diagonal | 6 cm |
Check the answer’s dimensions
An area contains a product of two lengths, while volume contains three. A perimeter or radius is still a length. If your input measurements are mixed between metres and centimetres, convert them to a common unit first. A realistic-looking number can still be wrong if the units were inconsistent.