Study Notes
The area is the amount of space a shape occupies in a two-dimensional plane. It can be calculated for various shapes using specific formulas.
- Area of a Rectangle — calculated by multiplying the length by the breadth. Example: If a rectangle has a length of 5 cm and a breadth of 3 cm, its area is 15 cm².
- Area of a Square — calculated by multiplying the length by itself. Example: If a square has a side length of 4 cm, its area is 16 cm².
- Area of a Composite Figure — found by breaking the figure into simpler shapes like rectangles or squares and summing their areas. Example: A shape made of two rectangles with areas 8 cm² and 12 cm² has a total area of 20 cm².
- Area of a Circle — calculated using the formula πr², where r is the radius. Example: A circle with a radius of 3 cm has an area of 28.26 cm² (using π ≈ 3.14).
- Area of a Triangle — calculated as 1/2 x base x perpendicular height. Example: A triangle with a base of 6 cm and height of 4 cm has an area of 12 cm².
- Area of a Parallelogram — calculated as base x perpendicular height. Example: A parallelogram with a base of 5 cm and height of 3 cm has an area of 15 cm².
- Area of a Trapezium — calculated as 1/2 x (sum of two parallel sides) x perpendicular height. Example: A trapezium with parallel sides of 4 cm and 6 cm, and height of 3 cm, has an area of 15 cm².
- Area of a Prism or Cylinder — calculated as the area of 2 bases plus the area of the curved surface. Example: A cylinder with radius 2 cm and height 5 cm has a surface area of 87.92 cm² (using π ≈ 3.14).
Exam Tips
Key Definitions to Remember
- Area of a Rectangle = Length x Breadth
- Area of a Square = Length x Length
- Area of a Circle = πr²
- Area of a Triangle = 1/2 x Base x Perpendicular Height
- Area of a Parallelogram = Base x Perpendicular Height
- Area of a Trapezium = 1/2 x (Sum of two parallel sides) x Perpendicular Height
- Area of a Prism or Cylinder = Area of 2 Bases + Area of Curved Surface
Common Confusions
- Confusing the formulas for area of a rectangle and a square
- Using diameter instead of radius in the circle area formula
- Forgetting to divide by 2 in the triangle area formula
Typical Exam Questions
- What is the area of a rectangle with length 8 cm and breadth 3 cm? Answer: 24 cm²
- How do you calculate the area of a circle with a radius of 5 cm? Answer: Use the formula πr², so the area is 78.5 cm² (using π ≈ 3.14)
- What is the area of a triangle with a base of 10 cm and height of 6 cm? Answer: 30 cm²
What Examiners Usually Test
- Correct application of area formulas for different shapes
- Ability to break down composite figures into simpler shapes
- Understanding the difference between radius and diameter in circle calculations