Geometry - Area - Rectangle, Square
Introduction
Area is a fundamental concept in Geometry. It refers to the measurement of the space occupied by a flat shape or an object on a plane surface.
Explanation Step by Step
To find the area, we calculate the total number of unit squares that fit inside a shape. It is always measured in square units like sq. cm or sq. m.
Sub-topics
Geometry - Area of Rectangle and Square
The area depends on the dimensions of the shape. For a rectangle, we use length and width. For a square, since all sides are equal, we use the length of one side.
Formulas
| Shape | Formula |
|---|---|
| Area of Rectangle | Length x Width |
| Area of Square | Side x Side (Side squared) |
Examples
Example 1
Find the area of a square with a side of 6 cm.
Area = Side x Side = 6 x 6
Answer: 36 sq. cm.
Tricks and Shortcuts
To quickly find the area of a square, just multiply the side value by itself (Squaring).
Common Mistakes
Forgetting to write 'square' in the unit. Always use sq. cm, sq. m, etc., for area results.
Practice Questions
Easy Questions
- Calculate the area of a rectangle with length 5 cm and width 3 cm.
- Find the area of a square whose side is 8 cm.
- A rectangular paper is 12 cm long and 4 cm wide. What is its area?
Medium Questions
- The area of a rectangle is 48 sq. cm. If the length is 8 cm, find the width.
- Find the side of a square whose area is 100 sq. m.
- A square room has a side of 5 meters. What is the area of the floor?
Hard Questions
- If the side of a square is doubled, by how many times does its area increase?
- A rectangular field is 50 m long and 30 m wide. How many square plots of side 5 m can be made in this field?
- A wire is bent into a square of side 10 cm. If the same wire is bent into a rectangle of length 12 cm, which shape has more area?
Revision Summary
Area = Surface covered. Rectangle: L x W. Square: S x S. Unit: Square units.
If the perimeter of a square is 24 cm, what is its area?
A
24 sq.cm
B
36 sq.cm
C
48 sq.cm
D
12 sq.cm
If the area of a rectangle and a square are equal (36 sq.cm), which one has the smaller perimeter?
A
Rectangle
B
Square
C
Both equal
D
Can't tell