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Srushti Ks from KENDRIYA VIDYALAYA, asked a question
Subject: Math , asked on 25/12/11

 the area of an equilateral triangle is 49 root 3 cm2taking each angular point as centre,circles are drawn with radii equal to half of the legth of the side of the triangle.find the area of the triangle not included in the circles. (take pi root3=1.73)

EXPERT ANSWER

S. Usha Rani , Meritnation Expert added an answer, on 31/12/13
705 helpful votes in Math
Let "a" be the side of equilateral triangle.

3 a 2 4 = 49 3 ; a 2 = 49 * 4 ; a =   7 * 2 = 14   c m ;
Radius of circle = 14/2 = 7 cm

Area of the first circle occupied by triangle = area of sector
= 1 2 r 2 θ = 1 2 * 7 2 * π * 60 180 = 77 3 c m 2
Area of all the 3 sectors = 77/3 * 3 = 77 cm2
Area of triangle not included in the circle
= area of triangle- area of all the 3 sectors
= = 49 3 - 77 = 7 . 87 c m 2

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Shri Agiwal From Kendriya Vidyalaya Bellary, added an answer, on 25/12/11
53 helpful votes in Math

 take pi = 22/7 and root 3 = 1.73

ar . of triangle = 49 root 3

root 3 /4 side sq. = 49 root 3

side sq. = 49 root 3 *4 /root 3 ( root 3 cancelled)

side sq. = 49*4 = 196

side = 14 cm

r = 14/2 (given)

r = 7cm

draw the fig . u wil get 3 sectors

ar of 1 sector = 77/3 cm sq. ( theta = 60)

ar 3 sectors = 77 /3 * 3 = 77cmsq ( 3 cancelled )

area of triangle not included  = ar of triangle - ar of 3 sectors

                                                   = 49*root3 - 77

                                                   = 49*1.73 - 77

                                                  = 84.77 - 77

                                                 = 7.77 cm sq. (777cm sq. is wrong ans)

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Lavanya Deogade From Kendriya Vidyalaya, added an answer, on 25/12/11
9 helpful votes in Math

 =1780.17-11r 2

           21

don 't know how to get the value of r .....sorry ....

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