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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)

Asked by Srushti Ks(student) , on 25/12/11

=1780.17-11r 2

21

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

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)

Posted by Shri Agiwal(student)on 25/12/11

Let "a" be the side of equilateral triangle.

$\frac{\sqrt{3}{a}^{2}}{4}=49\sqrt{3};\phantom{\rule{0ex}{0ex}}{a}^{2}=49*4;\phantom{\rule{0ex}{0ex}}a=7*2=14cm;$
Radius of circle = 14/2 = 7 cm

Area of the first circle occupied by triangle = area of sector
$=\frac{1}{2}{r}^{2}\theta =\frac{1}{2}*{7}^{2}*\pi *\frac{60}{180}=\frac{77}{3}c{m}^{2}$
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
=$=49\sqrt{3}-77=7.87c{m}^{2}$

Posted by S. Usha Rani(MeritNation Expert)on 31/12/13

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