Chapter 12: Areas Related to Circles

In Class 10 Maths, Chapter 12, Areas Related to Circles, we will learn about the concepts related to the areas of different figures like circles, sectors, and segments.

Introduction:
- The area of a circle is the region enclosed by its circumference.
- The formula to calculate the area of a circle is A = πr², where 'A' represents the area and 'r' represents the radius of the circle.
- The value of π is approximately 3.14 or can be taken as 22/7.

Areas of Sectors:
- A sector of a circle is a region enclosed by two radii of the circle and the corresponding arc.
- The formula to calculate the area of a sector is A = (θ/360) × πr², where 'θ' represents the angle formed by the two radii.

Areas of Segments:
- A segment of a circle is a region enclosed by an arc and a chord.
- To find the area of a segment, we need to subtract the area of the triangle formed by the chord and the two radii from the area of the sector.
- The formula to calculate the area of a segment is A = (θ/360) × πr² - (1/2) × r² × sin(θ), where 'θ' represents the angle formed by the two radii.

Areas of Combinations of Plane Figures:
- We can find the area of a combination of plane figures by adding or subtracting the areas of individual figures.
- For example, to find the area of a figure formed by a circle and a rectangle, we can calculate the area of the circle and the rectangle separately and then add them.

Applications:
- The concepts of areas related to circles have various applications in real-life scenarios, such as calculating the area of a circular garden or a sector of a pizza.
- These concepts are also used in fields like architecture, engineering, and design.

Summary:
- In this chapter, we have learned about the areas of circles, sectors, and segments.
- We have also understood how to calculate the area of combinations of plane figures.
- These concepts have practical applications in various fields and are important for a better understanding of geometry.