Area comes from multiplying measurements and perimeter from adding them. A rectangle 4/3 m by 3/8 m has an area of 1/2 m² and a perimeter of 41/12 m, in different units. If you are asked for the area, the product is handled by the multiply fractions calculator; if you are asked for the perimeter, adding the sides is done by the add fractions calculator.
| You are asked for | Operation | Unit |
|---|---|---|
| Area of a rectangle | Base × height | m², cm² |
| Area of a square | Side × side | m², cm² |
| Area of a triangle | Base × height ÷ 2 | m², cm² |
| Perimeter of a rectangle | 2 × (base + height) | m, cm |
| Perimeter of a triangle or a square | Sum of the sides, or 4 × side | m, cm |
| One side, given the area and the other side | Area ÷ known side | m, cm |
The table separates the two worlds: what you multiply gives a surface, and what you add gives a length. In a triangle, the height is the perpendicular distance to the base, not the slanted side.
Why area has square units
Multiplying two lengths gives a surface, which is why meters times meters give square meters. Divide the rectangle into a grid with columns of half a meter and rows of 1/4 m. Each cell covers 1/8 of a square meter, and 5 × 3 = 15 cells fit. That count is the multiplication of numerators and of denominators.
Perimeter, on the other hand, runs along the edge and measures length, so it stays in meters. If an area appears in meters rather than square meters, the square has been lost. The fraction visualizer lets you draw other models of this kind.
Worked example: a rectangle in meters
A rectangle is 2 1/2 m long and 3/4 m wide. Find its area and perimeter.
- Convert the mixed number. 2 × 2 + 1 = 5, so 2 1/2 = 5/2.
- Multiply for the area. (5 × 3)/(2 × 4) = 15/8, which is already in lowest terms.
- Add the two sides. With denominator 4, 5/2 is 10/4, and 10/4 + 3/4 = 13/4.
- Double for the perimeter. 2 × 13/4 = 26/4 = 13/2.
Result: area 1 7/8 m², perimeter 6.5 m.
Check: in decimals, 2.5 × 0.75 = 1.875, and 15 ÷ 8 gives the same. For the perimeter, 2 × (2.5 + 0.75) = 6.5.
How to find the area of a composite shape
Split the shape into rectangles, or subtract a piece from a larger rectangle. Picture a plywood panel 3 m by 2 m with a notch of 3/2 m by 1/2 m missing at one corner. The full rectangle is 3 × 2 = 6 m², the notch takes up 3/2 × 1/2 = 3/4 m², and the panel measures 6 − 3/4 = 21/4 m², or 5 1/4 m².
The perimeter has a trick: it equals that of the full rectangle, 2 × (3 + 2) = 10 m. Cutting off the corner removes 3/2 m of edge along the top and half a meter along one side, but two new stretches of those same lengths appear inside the notch. That only happens when the notch touches the corner. If the piece is cut out of the middle of a side, the perimeter increases.
To convert mixed numbers by hand or check your conversion, use mixed numbers or mixed number to fraction.
How to find a missing side
With the area and one side, the other side is the area divided by the known side. If the area is 9/10 m² and one side is 3/5 m, the other is 9/10 ÷ 3/5. Dividing by a fraction is multiplying by its reciprocal, so 9/10 × 5/3 = 45/30 = 3/2 m. The divide fractions calculator does that inversion.
With the perimeter the route is different. Divide the perimeter by 2 to get the sum of two adjacent sides, then subtract the side you know. With a perimeter of 11/2 m and one side of 7/4 m, the sum of two sides is 11/4, and 11/4 − 7/4 = 1, so the other side is 1 m. If you get a side longer than half the perimeter, there is a mistake in the calculation.
Practice with two rectangles
Practice
- Find the area of a rectangle 7/2 m by 2/3 m.
- Find its perimeter.
- A rectangle has an area of 5/6 m² and one side of 5/9 m. How long is the other side?
See the answers
- 7/2 × 2/3 = 14/6 = 7/3 m², or 2 1/3 m².
- 7/2 + 2/3 = 21/6 + 4/6 = 25/6, and double that is 25/3 m, or 8 1/3 m.
- 5/6 ÷ 5/9 = 5/6 × 9/5 = 45/30 = 3/2 m.
Check the result and keep going
Before accepting an answer, check three things: the area is in square units, the perimeter is greater than the longest side, and the result matches a decimal estimate. The guide on verifying a fraction answer gathers more techniques. If the measurements are in inches, see how to add fractional inches. If what you need is a part of a quantity rather than a shape, use fraction of a number.
For the definition of perimeter as the sum of the side lengths of a polygon, see the Wikipedia entry Perimeter (accessed October 17, 2026). That source does not cover fractions: the fraction calculations are the ones worked out on this page.