Rectangle area and perimeter
A rectangle is one of the most common shapes in geometry. Two formulas cover every rectangle question: one for the space inside the shape and one for the distance around it. Mastering both — and knowing how to rearrange them — lets you find any missing value.
Core formulas
Area: A = l × w
Perimeter: P = 2(l + w) = 2l + 2w
where l = length and w = width
Parts of a rectangle
A rectangle has four sides and four right angles. The two longer sides have the same length, and the two shorter sides have the same width. Length (l) and width (w) are the only two measurements you need for any rectangle calculation.
Note: length and width are relative labels — some problems use base and height instead. The formulas work the same way regardless of the labels.
Two formulas, four question types
Both formulas can be rearranged to find any missing value. There are exactly four question types you will encounter.
Find area (know l and w)
A = l × w
Find perimeter (know l and w)
P = 2 × (l + w)
Find missing side (know area + one side)
missing side = A ÷ known side
Find missing side (know perimeter + one side)
missing side = (P ÷ 2) − known side
Area vs perimeter: which to use?
- Area measures the flat space inside the rectangle — used when tiling a floor, painting a wall, or calculating the size of a garden bed. Units are always squared (cm², m², ft²).
- Perimeter measures the total distance around the outside edge — used when fencing a yard, framing a picture, or bordering a room with trim. Units are linear (cm, m, ft).
- If a problem mentions covering, filling, or material needed for the surface, it is asking for area.
- If a problem mentions going around, fencing, bordering, or the edge, it is asking for perimeter.
Worked examples
Example 1: find the area
A rectangle has a length of 12 cm and a width of 5 cm. Find the area.
A = l × w = 12 × 5 = 60 cm²
Multiply the two given dimensions. The unit is always squared when finding area.
Example 2: find the perimeter
A rectangle has a length of 9 m and a width of 4 m. Find the perimeter.
P = 2 × (l + w) = 2 × (9 + 4) = 2 × 13 = 26 m
Add the two sides first, then multiply by 2 — or double each side and add: 2(9) + 2(4) = 18 + 8 = 26. Both routes give the same answer.
Example 3: find a missing side using area
A rectangle has an area of 48 ft² and a width of 6 ft. Find the length.
A = l × w → l = A ÷ w = 48 ÷ 6 = 8 ft
Rearrange the area formula by dividing both sides by the known dimension. Always divide, never multiply, when working backward from area.
Example 4: find a missing side using perimeter
A rectangle has a perimeter of 30 in and a length of 10 in. Find the width.
P = 2(l + w) → l + w = P ÷ 2 = 30 ÷ 2 = 15
w = 15 − l = 15 − 10 = 5 in
First halve the perimeter to get the sum of one length and one width. Then subtract the known side to get the unknown.
Related shape: the square
A square is a special rectangle where length and width are equal (l = w = s). Its area and perimeter formulas simplify because of that equal-side constraint.
Rectangle (general)
A = l × w
P = 2(l + w)
Square (l = w = s)
A = s²
P = 4s
Refreshable sample
Try one rectangle question
Work through the problem before checking. The widget generates a different question each time you refresh.
Common mistakes to avoid
- Adding instead of multiplying for area. A = l + w gives the wrong answer. Area always requires multiplication of the two dimensions.
- Forgetting to double when finding perimeter. P = l + w only counts two sides. The correct formula is P = 2(l + w) because a rectangle has two pairs of equal sides.
- Using the wrong operation when finding a missing side. To reverse the area formula, divide (not subtract). To reverse the perimeter formula, halve first, then subtract.
- Mixing up area and perimeter units. Area is in square units (cm²). Perimeter is in linear units (cm). Writing cm when you mean cm² is a common error on exams.
- Swapping length and width. It does not matter which side you call length or width as long as you are consistent within one problem. Swapping mid-calculation breaks the result.