Table of contents  
Perimeter and Area of a Circle  
Perimeter and Area of the Semicircle  
Area of a Ring  
Areas of Sectors of a Circle  
Length of an Arc of a Sector of Angle θ 
The perimeter of all the plain figures is the outer boundary of the figure. Likewise, the outer boundary of the circle is the perimeter of the circle. The perimeter of circle is also called the Circumference of the Circle.
Circumference = 2πr = πd (π = 22/7)
r = Radius and d = 2r
The area is the region enclosed by the circumference.
Area of the circle = πr^{2}
Example: If a pizza is cut in such a way that it divides into 8 equal parts as shown in the figure, then what is the area of each piece of the pizza? The radius of the circle shaped pizza is 7 cm.
Solution: The pizza is divided into 8 equal parts, so the area of each piece is equal.
Area of 1 piece = 1/8 of area of circle
The perimeter of the semicircle is half of the circumference of the given circle plus the length of diameter as the perimeter is the outer boundary of the figure.
Area of the semicircle is just half of the area of the circle.
Area of the ring i.e. the coloured part in the above figure is calculated by subtracting the area of the inner circle from the area of the bigger circle.Where, R = radius of outer circle
r = radius of inner circle
The area formed by an arc and the two radii joining the endpoints of the arc is called Sector.
Remark: Area of Minor Sector + Area of Major Sector = Area of the Circle
An arc is the piece of the circumference of the circle so an arc can be calculated as the θ part of the circumference.
The area made by an arc and a chord is called the Segment of the Circle.
The area made by chord AB and arc X is the minor segment. The area of the minor segment can be calculated by
Area of Minor Segment = Area of Minor Sector – Area of ∆ABO
The other part of the circle except for the area of the minor segment is called a Major Segment.
Area of Major Segment = πr^{2}  Area of Minor Segment
Remark: Area of major segment + Area of minor segment = Area of circle
As we know how to calculate the area of different shapes, so we can find the area of the figures which are made with the combination of different figures.
Solution: Given
ABC is an equilateral triangle, so ∠A, ∠B, ∠C = 60°
Hence the three sectors are equal, of angle 60°.
Required
To find the area of the shaded region.
Area of shaded region =Area of ∆ABC – Area of 3 sectors
Area of ∆ABC = 17320.5 cm^{2}
Side = 200 cm
As the radius of the circle is half of the length of the triangle, so
Radius = 100 cm
Area of 3 Sectors = 3 × 15700/3 cm^{2} cm^{2}
Area of shaded region = Area of ∆ABC – Area of 3 sectors
= 17320.5  15700 cm^{2}
= 1620.5 cm^{2}
Example: Find the area of the shaded part, if the side of the square is 8 cm and the 44 cm.
Solution: Required region = Area of circle – Area of square
= πr^{2} – (side)^{2}
Circumference of circle = 2πr = 44
Radius of the circle = 7 cm
Area of circle = πr^{2}
Area of square = (side)^{ 2} = (8)^{2} = 64 cm^{2}
Area of shaded region = Area of circle – Area of square
= 154 cm^{2}  64 cm^{2}
= 90 cm^{2}
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1. What is the formula for finding the perimeter of a circle? 
2. How do you calculate the area of a semicircle? 
3. How can you find the area of a ring with inner radius r1 and outer radius r2? 
4. What is the formula for calculating the area of a sector of a circle with angle θ? 
5. How do you find the length of an arc of a sector with angle θ and radius r? 

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