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.
Two diagonals
Given: Diagonal p = 6; Diagonal q = 8.
A = pq/2; a = √(p²+q²)/2
| Measurement | Calculated value |
|---|---|
| Area | 24 cm² |
| Side | 5 cm |
| Perimeter | 20 cm |
| Height | 4.8 cm |
Side and interior angle
Given: Side a = 5; Interior angle θ = 60.
A = a² sin θ; P = 4a
| Measurement | Calculated value |
|---|---|
| Side | 5 cm |
| Area | 21.650635 cm² |
| Perimeter | 20 cm |
| Diagonal across angle | 5 cm |
| Other diagonal | 8.660254 cm |
| Height | 4.330127 cm |
Side and height
Given: Side a = 5; Perpendicular height h = 4.
A = ah; θ = arcsin(h/a)
| Measurement | Calculated value |
|---|---|
| Side | 5 cm |
| Area | 20 cm² |
| Perimeter | 20 cm |
| Diagonal across angle | 4.472136 cm |
| Other diagonal | 8.9442719 cm |
| Height | 4 cm |
Area and interior angle
Given: Area A = 25; Interior angle θ = 60.
a = √(A/sin θ)
| Measurement | Calculated value |
|---|---|
| Side | 5.3728497 cm |
| Area | 25 cm² |
| Perimeter | 21.491399 cm |
| Diagonal across angle | 5.3728497 cm |
| Other diagonal | 9.3060486 cm |
| Height | 4.6530243 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.