Definitions [1]
Area of a circle: The area of a circle is the region occupied by the circle in a two-dimensional plane.
Formulae [7]
Perimeter of a Triangle = 3 × length of a side.
Perimeter of a rectangle = 2 × length + 2 × breadth
P = 2(1 + b) ⇒ (i) l = `P/2` − b, i.e., length = `"Perimeter"/2` − breadth
(ii) l = `P/2` − l, i.e., breadth = `"Perimeter"/2` − length
Perimeter of Square = Total boundary of the square
= Side + Side + Side + Side
P = 4 × Side
Or: P = 4s (where 's' represents the side length)
side = ` "perimeter"/"4"`
Always include the correct linear unit (cm, m, mm, km, etc.)
Area of the trapezium = `1/2` × sum of the lengths of parallel sides × height.
Area of parallelogram = base x height
- Area of a rhombus = `1/2` x product of lengths of diagonals.
Area of the circle = πr2
Theorems and Laws [1]
If three circles of radius a each, are drawn such that each touches the other two, prove that the area included between them is equal to `4/25 a^2`. [Take `sqrt(3) = 1.73` and π = 3.14.]
When three circles touch each other, their centres form an equilateral triangle, with each side being 2a.
Area of the triangle`=sqrt(3)/4xx2"a"xx2"a" = sqrt(3)"a"^2`
Total area of the three sectors of circles `=3xx60/360xx22/7xx"a"^2 = 1/2xx22/7 "a"^2 = 11/7"a" ^2`
Area of the region between the circles = Area of the triangle - Area of three sectors
`=(sqrt(3)-11/7)"a"^2`
= (1.73 - 1.57)a2
= 0.16 a2
= 0.16 a2
`=4/25"a"^2 `
