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

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 • 72 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

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

= 3(60/360 * 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

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guys thankyou.....

• -4

what matttttttt  said is correct.

• -8

1620.5 cm2is the area of the shaded region! :D

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• -6 • 15

say: ABC is an equilateral triangle.

as all angles equals  60°

Area of ΔABC = 17320.5

side= a

as we know √3/4.(side)²  = 17320.5

(a)²  = 17320.5 × 4/1.73205

(a)²  = 4 × 104

a  = 200 cm

Radius of the circles = 200/2 cm = 100 cm

Area of 1 sector = (60°/360°) × π r²

= 1/6 × 3.14 × (100)²

= 15700/3

Area of 3 sectors = 3 × 15700/3 = 15700

Area of the shaded region = Area of equilateral ΔABC - Area of 3 sectors

= 17320.5 - 15700

= 1620.5

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