Area Calculator guide
How to Find the Area of a Rhombus
The easiest way to find the area of a rhombus is to multiply its two diagonals together and divide by two: A = (p × q) ÷ 2. For diagonals of 10 and 8, the area is (10 × 8) ÷ 2 = 40. If you know the base and perpendicular height instead, A = b × h also works.
What makes a shape a rhombus
A rhombus has four sides, all the same length, with opposite sides parallel. A square is a rhombus that happens to have right angles; a rhombus in general is a square that has been pushed over to one side.
The property that matters for finding its area is this: the two diagonals cross each other at right angles, and each one cuts the other exactly in half. That is what makes the diagonal formula work.
Method 1 — from the diagonals
A = (p × q) ÷ 2, where p and q are the lengths of the two diagonals.
With diagonals of 10 and 8: A = (10 × 8) ÷ 2 = 80 ÷ 2 = 40 square units.
This is usually the easier route, because diagonals are often the measurement you actually have — particularly if you are measuring a physical object rather than reading numbers off a diagram.
Why halving the product works
Draw a rectangle around your rhombus, with the rhombus's four corners touching the middle of each of the rectangle's sides.
That rectangle has width p and height q, so its area is p × q. And the rhombus takes up exactly half of it — the four leftover corner triangles fit together to make a second, identical rhombus.
So the rhombus is half of p × q, which is the formula.
Method 2 — base times height
A rhombus is a special parallelogram, so the parallelogram formula works too: A = b × h, where b is any side and h is the perpendicular height.
The catch is the same one as with the trapezoid: h is the straight-across distance between two parallel sides, not the length of the side itself. If you use the side length, you will get the area of a square instead — which is always too big unless the rhombus really is a square.
Use this method when you have been given a height. Use the diagonal method otherwise.
Finding the perimeter
All four sides of a rhombus are equal, so the perimeter is just four times one side.
If you only have the diagonals, you can still get there. The diagonals cut each other in half and meet at right angles, so each side of the rhombus is the hypotenuse of a right triangle with legs of p÷2 and q÷2.
For our example: half-diagonals of 5 and 4, so each side is √(5² + 4²) = √41 ≈ 6.403. The perimeter is 4 × 6.403 = about 25.61.
The calculator does this for you, which is why it can give you a perimeter from diagonals alone.
