Area of rectangles and parallelograms
key notes :
| Area of a Rectangle |
Definition: A rectangle is a quadrilateral with opposite sides equal and all angles equal to 90°.
Formula:
Area of Rectangle=Length×Breadth
Explanation: The area is the amount of surface covered inside the rectangle.
Units: square units (cm², m², etc.).
✅ Examples:
A rectangle of length 12 cm and breadth 5 cm
- Are = 12×5=60 cm2
A rectangle of length 8 m and breadth 3 m
- Area = 8×3=24 m2
| Area of a Parallelogram |
Definition: A parallelogram is a quadrilateral with both pairs of opposite sides parallel and equal.
Formula:
Area of Parallelogram=Base×Height
Note: The height is the perpendicular distance between the two parallel sides (not the slant side).
✅ Examples:
A parallelogram with base 10 cm and height 6 cm
- Area=10×6=60 cm2
A parallelogram with base 15 m and height 8 m
- Area=15×8=120 m2
| Key Differences |
| Shape | Formula | Important Note |
|---|---|---|
| Rectangle | Length × Breadth | Sides are perpendicular |
| Parallelogram | Base × Height | Height must be perpendicular to base |
| Important Points |
- The area of a parallelogram is equal to the area of a rectangle with the same base and height.
- Always check whether the given measurement is the perpendicular height, not the slant side.
- Units must be written (cm², m², etc.).
| Practice Questions |
- Find the area of a rectangle of length 14 cm and breadth 9 cm.
- A parallelogram has a base of 12 m and height of 7 m. Find its area.
- The area of a rectangle is 72 m². If its length is 12 m, find its breadth.
- A parallelogram has sides 8 cm and 6 cm, with the height corresponding to base 8 cm being 5 cm. Find its area.
Learn with an example
➡️ What is the area?
______ square millimetres
Find the base and height of the rectangle.
base: 8 mm
height: 10 mm
Use these numbers in the formula.
area=base
height=8.10
=80
Now find the units. The lengths are measured in millimetres, so the area is measured in square millimetres.
The area is 80 square millimetres.
➡️ What is the missing length?
area=2 m2
w= ______ metres
Find the base, height and area of the rectangle.
base: w
height: 2 m
area: 2 m2
Use the formula:
area=base . height
2=w . 2
1=w
Now look for the units. The area is measured in square metres, so lengths are measured in metres. So, w=1 metre.
➡️ What is the area?
______ square metres
Find the base and height of the rectangle.
base: 7 m
height: 8 m
Use these numbers in the formula.
area = base . height
=7 . 8
=56
Now find the units. The lengths are measured in metres, so the area is measured in square metres.
The area is 56 square metres.
Let’s practice!🖊️
