Question

formule of chapter 12 for class 10 maths​

Answer 1

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:

L= (θ/360°)×2πr

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

(θ/360°)×πr2

where ∠θ is the angle of this sector(minor sector in the following case) and r is its radius

Area related to circles class 10 -1

Area of a sector

To know more about Sector of a Circle, visit here.

Area of a Triangle

The Area of a triangle is,

Area=(1/2)×base×height

If the triangle is an equilateral then

Area=(√3/4)×a2 where “a” is the side length of the triangle.

To know more about Area of a Triangle, visit here.

Area of a Segment of a Circle

Area related to circles class 10 -2

Area of segment APB (highlighted in yellow)

= (Area of sector OAPB) – (Area of triangle AOB)

=[(∅/360°)×πr2] – [(1/2)×AB×OM]

[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.

=[(θ/360°)×πr2] – [r2×sin θ/2 × cosθ/2]

Where θ is the angle of the sector and r is the radius of the circle

Visualizations

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 the perpendicular height.

Area related to circles class 10 -3

parallelogram

Area of a trapezium =[(a+b)×h]/2,

where

a & b are the length of the parallel sides

h is the trapezium height

Area of a rhombus =pq/2, where p & q are the diagonals.

Answer 2

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Circumference of a Circle or Perimeter of a Circle:

•The distance around the circle or the length of a circle is called its circumference or perimeter.

•Circumference (perimeter) of a circle = πd or 2πr,

where d is a diameter and r is a radius of the circle and π = 22/7

•Area of a circle = πr²

•Area of a semicircle = 1/2 πr²

•Area of quadrant = ¼ πr²

•Area of the ring or an annulus = πR² – πr²

= π(R² – r²)

= π (R + r) (R – r)

•Perimeter of a semicircle or protractor = πr + 2r

•Length of the arc AB = 2πrθ/360° = πrθ/180°

•Area of sector = πr2θ/360°

Area of sector = 1/2 (r × l).

•Perimeter of sector= Length of arc + 2r= πrθ/180°+ 2r