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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. - CBSE Class 10 - Mathematics

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Question

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 `sqrt3 `= 1.73205]

Solution

Let the side of the equilateral triangle be a.

Area of equilateral triangle = 17320.5 cm2

sqrt3/4(s)^2 = 17320.5

1.7320/4a^2 = 17320.5

a2 = 4 x 10000

a = 200 cm

Each sector is of measure 60°.

Area of sector ADEF = `60^@/360^@ xx pixxr^2`

`=1/6xxpixx(100)^2`

`=(3.14xx10000)/6`

`= 15700/3 cm^2`

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

`= 17320.5 - 3xx 15700/3`

= 17320.5-15700 = 1620.5 cm2

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 12: Areas Related to Circles
Ex. 12.30 | Q: 10 | Page no. 236
Solution 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. Concept: Areas of Combinations of Plane Figures.
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