# Polygon , Circle , Rooms , Sector & Segment | mensuration short tricks.

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Today we are going to talk about the some Important arithmetic formulae on polygon , circles , Room and sector & segment. Here you can access list of all the formulae at one place.

Students are advised to learn all the formulae and keep practicing with it.

SOME IMPORTANT SUTRAS

* POLYGON
1). Each internal angle of the regular polygon =
180(n-2)/n
2). Perimeter of regular polygon = n×a
3). Perimeter of regular hexagons = 6×sides
4). Area of regular hexagons = (6√3/4)×side^2
5). Sum of all the internal angles of n sided polygon = 180(n-2)
6). Every external angle of n sided regular polygon = 360/n
7). Area of regular polygon = n×a×h/2
8). Areas of regular polygon = na^2.cot(π/2)/4
9). Length of the perpendicular drawn from the centre of the regular polygon to the side is =
a.tan(θ/2)/2
10). Length of the perpendicular drawn from the centre of the regular polygon to the side is =
a.cot(π/n)/2
11). No of diagonals of n sided regular polygon =
n(n-3)/2
* CIRCLES
1). Area of circles = πr^2
2). Area of circles = πd^2/4
3). Area of semicircle = πr^2/2
4). Radius of circle = √A/π
5). Circumference of circle = 2πr = πd
6). Radius of circle = circumference/2π
7). Diameter of circle = circumference/π
8). Circumference of semicircle = (π+2).r
9). Area of flat rings = π(R^2-r^2)
10). Area of biggest triangle formed in the semicircle of radius r = r^2
* ROOMS
1). Area of the surface of the room = l.b
2). Area of four wall = 2(l+b).h
3). Area of room’s roof = l.b
4). No. Of bricks = l×b/area of one bricks
5). Cost of area = area×cost of unit area
6). Area = total cost/cost per unit
* SECTOR & SEGMENT
1). Area of sector = πr^2θ/360
2). Area of sector = l×r/2
3). Length of arc = 2πrθ/360
4). Perimeter of sector = 2πrθ/360 + 2r
5). Angle of the sector = 360×A/πr^2
6). Area of major segment =
πr^2.(360-θ)+r^2.sinθ/2
7). Area of minor segment =
πr^2.θ/360-r^2.sinθ/2
8). Perimeter of minor segment =
2πr.θ/360+2r.sinθ/2
9). The largest side of square in the circle = √2.r
10). Area of the largest square in the circle = 2r^2
= D^2/2
11). Area of major sector = πr^2(360-θ)/360