how to find the area of a rectangle
To find the area of a rectangle, multiply its length by its width: Area=length×width\text{Area}=\text{length}\times \text{width}Area=length×width.
What “area of a rectangle” means
Area tells you how much space is inside the rectangle’s boundary.
If you imagine the rectangle made of 1-by-1 little squares, the area is how many of those squares fit inside.
The core formula (super quick)
For any rectangle:
Area=length×width\text{Area}=\text{length}\times \text{width}Area=length×width
- Length: one side (usually the longer side).
- Width (or breadth): the side next to it.
- Units: if sides are in cm, area is in square cm (cm²); if in m, area is in m².
Example:
A rectangle is 5 cm long and 6 cm wide.
Area = 5 × 6 = 30 cm².
Step‑by‑step method
- Identify the length and width from the problem or diagram.
- Make sure both are in the same unit (both in cm, or both in m, etc.).
- Multiply them: length × width.
- Attach “square” to the units (cm², m², etc.).
If you know different information
Sometimes you are not given both sides directly but you can still find the area.
1. Using diagonal and one side
If you know:
- Diagonal ddd
- One side, say length lll
Then:
- Find the other side (width www) using Pythagoras:
w=d2−l2w=\sqrt{d^{2}-l^{2}}w=d2−l2
2. Then area = l×wl\times wl×w.
Example:
Diagonal 10 units, length 8 units.
Width =
102−82=100−64=36=6\sqrt{10^{2}-8^{2}}=\sqrt{100-64}=\sqrt{36}=6102−82=100−64=36=6.
Area = 8 × 6 = 48 square units.
2. Using perimeter and one side
Perimeter PPP of a rectangle is P=2(l+w)P=2(l+w)P=2(l+w).
If you know the perimeter and one side, you can find the other:
- Use P=2(l+w)P=2(l+w)P=2(l+w) to solve for the missing side.
- Then multiply length × width for area.
Example:
Perimeter = 30 units, width = 4 units.
From 30=2(l+4)30=2(l+4)30=2(l+4) → l=11l=11l=11 units.
Area = 11 × 4 = 44 square units.
Mini “Quick Scoop” recap
- Formula: Area of a rectangle = length × width.
- Both measurements must be in the same unit (like all in cm or all in m).
- Answer is always in square units (cm², m², etc.).
- If you only know diagonal + one side or perimeter + one side, you can first find the missing side, then use the same formula.
If you send a specific rectangle (like “length 12 cm, width 7 cm”), I can walk through the exact calculation for that example.
Information gathered from public forums or data available on the internet and portrayed here.