Topics
Number Systems
Number Systems
Polynomials
Algebra
Algebraic Expressions
Algebraic Identities
Coordinate Geometry
Linear Equations in Two Variables
Coordinate Geometry
Geometry
Area
Constructions
- Introduction of Constructions
- Geometric Constructions
- Some Constructions of Triangles
Introduction to Euclid’S Geometry
Mensuration
Statistics and Probability
Lines and Angles
- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Parallel Lines
- Concept of Pairs of Angles
- Concept of Transversal Lines
- Basic Properties of a Triangle
Probability
Triangles
Quadrilaterals
- Properties of Quadrilateral
- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
Circles
Areas - Heron’S Formula
- Area of a Triangle by Heron's Formula
- Application of Heron’s Formula in Finding Areas of Quadrilaterals
- Geometric Interpretation of the Area of a Triangle
Surface Areas and Volumes
Statistics
- Introduction
- Formula: Area
- The Standard Unit of Area
- Example
Introduction
Area is one of the most fundamental ideas in geometry. Simply put, Area is the measure of how much two-dimensional space a flat, closed shape takes up.
Imagine you are covering a floor with tiles or painting a wall. The amount of paint or the number of tiles you need is determined by the area of that surface. Understanding area is essential for many real-world tasks, from architecture and construction to gardening and design.
Formula: Area
Area = Amount of space inside a flat shape
The Standard Unit of Area
To measure area, we use a standard unit.
Because area has length × width, the unit is always a square.
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A square with side 1 unit is the basic unit of area.
How We Write Area Units
Area units are written as square units or with a small raised 2 (²).
- If the side is 1 centimeter, the area is 1 square centimeter (1 cm²).
- If the side is 1 meter, the area is 1 square meter (1 m²).
- If the side is 1 kilometer, the area is 1 square kilometer (1 km²).
Example
Of the figures given above, figure ABCD has six squares of 1 cm each inside it. It means that its area is 6 sq cm.
In the same way, count the squares in each figure and write its area.
- Area of MNRS = 9 sq cm
- Area of EFGH = 4 sq cm
- Area of PQRS = 5 sq cm
- Area of IJKL = 8 sq cm
Example Question 1
By counting squares, estimate the area of the figure.
| Covered area | Number |
Area estimate |
| (i) Fully-filled squares | 11 | 11 |
| (ii) Half-filled squares | 3 | `3 xx 1/2` |
| (iii) More than half-filled squares | 7 | 7 |
| (iv) Less than half-filled squares | 5 | 0 |
Total area = 11 + 3 × `1/2 + 7 = 19 1/2` sq units.
Example Question 2
By counting squares, estimate the area of the figure.
| Covered area | Number | Area estimate (sq units) |
| (i) Fully-filled squares | 1 | 1 |
| (ii) Half-filled squares | - | - |
| (iii) More than half-filled squares | 7 | 7 |
| (iv) Less than half-filled squares | 9 | 0 |
Total area = 1 + 7 = 8 sq units.
