Get the complete notes on an area related to circles for class 10 is provided here. The concepts related to circles such as area, circumference, segment, sector, angle and length of a circle, area for the sector of a circle is provided here. Also, the visualization of some plane and solid figures areas are discussed here.
Area of a Circle
Area of a circle is πr2, where π=22/7 or ≈3.14 (can be used interchangeably for problem-solving purposes)and r is the radius of the circle.
π is the ratio of the circumference of a circle to its diameter.
Circumference of a circle
The perimeter of a circle is the distance covered by going around its boundary once. The perimeter of a circle has a special name: CIrcumference, which is π times the diameter which is given by the formula 2πr
The segment of a circle
A circular segment is a region of a circle which is “cut off” from the rest of the circle by a secant or a chord
A sector of a circle
A circle sector/ sector of a circle is defined as the region of a circle enclosed by an arc and two radii. The smaller area is called the minor sector and the larger area is called the major sector.
The angle of a Sector
The angle of a sector is that angle which is enclosed between the two radii of the sector.
Length of an arc of a sector
The length of the arc of a sector can be found by using the expression for the circumference of a circle and the angle of the sector, using the following formula:
where θ is the angle of sector and r is the radius of the circle.
Area of a Sector of a Circle
Area of a sector is given by
where ∠θ is the angle of this sector(minor sector in the following case) and r is its radius
Area of a Triangle
Area of a triangle is,
If the triangle is an equilateral then
Area=√4×a2 where a is the side of the triangle.
Area of a Segment of a Circle
Area of segment APB (highlighted in yellow)
= (Area of sector OAPB) – (Area of triangle AOB)
[To find the area of triangle AOB, use trigonometric ratios to find OM (height) and AB (base)]
Also, Area of segment APB can be calculated directly if the angle of the sector is known using the following formula.
where θ is the angle of the sector and r is the radius of the circle
Areas of different plane figures
– Area of a square (side l) =l2
– Area of a rectangle =l×b, where l and b are the length and breadth of the rectangle
– Area of a parallelogram =b×h, where b is the base and h is perpendicular height.
Area of a trapezium =[(a+b)×h]/2,
a & b are the parallel sides length
h is the trapezium height
Area of a rhombus =pq/2, where p & q are the diagonals
Areas of Combination of Plane figures
For example: Find the area of the shaded part in the following figure: Given the ABCD is a square of side 28cm and has four equal circles enclosed within.
– Looking at the figure we can visualise that the required shaded area = A(square ABCD) − 4 ×A(Circle).
– Also, the diameter of each circle is 14 cm.