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The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (See the given figure). Find the area of shaded region. [Use π = 3.14 and\"\"]

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plz answer this question....and plz tell me step by step......can anyone...help me..

Asked by Anushka Das(student) , 6 days, 4 hours ago


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Let the side of the equilateral triangle be a.

Area of equilateral triangle = 17320.5 cm2

Each sector is of measure 60°.

Area of sector ADEF 

Area of shaded region = Area of equilateral triangle − 3 × Area of each sector

Posted by Mohil(student)on 1/2/12

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area of ABC = 1.743205/4 a2

17320.5 = 1.73205/4 a2

a2 = 17320.5 * 4 / 1.73205

a2 = 10000 * 4

 a2 = 40000

a = 200cm

radius = a/2

 radius = 100 cm

area of three sectors = 3( theta/360 pie r2)

= 3(6 0/360 * 3.14 * 100  *100)

= 3(1/6 * 314 * 100)

=134*50

= 15700cm2

area of shaded region = aria of ABC - areaof three sectors

area of shaded region = 17320.5 - 15700

area of shaded region = 1620.5 cm2

Posted by Thunder Storm(student)on 1/2/12

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 what matttttttt  said is correct.

Posted by Sathish Kumar(student)on 2/2/13

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1620.5 cm2is the area of the shaded region! :D

Posted by Namrata Bhirud(student)6 days, 3 hours ago

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