In given figure the area of an equilateral triangle ABC is 17320.5cm2. With each vertex of the triangle as a center, a circle is drawn with a radius equal to half the length of the side of the triangle. Find the area of the shaded region. (Use π=3.14 and 3=1.73205)

Question

In given figure the area of an equilateral triangle ABC is 17320.5cm2. With each vertex of the triangle as a center, a circle is drawn with a radius equal to half the length of the side of the triangle. Find the area of the shaded region. (Use π=3.14 and 3​=1.73205)

Filo · Accepted Answer

Given AB=BC=ACArea of Equilateral △ ABC = 17320.5cm2                  ∴ 43​​×AB2 =17320.5                     ∴ AB =200cmAlso, AB=2AD∴     AD=100 cm =radiusArea of sector DAE + Area of sector DBF + Area of sector FCE We know that area of sector =360θ​×π×r2=3×36060​×3.14×100×100=15700cm2∴   Area of the shaded region = Area of equilateral triangle − Area of all sectors                                          =17320.5−15700                                          =1620.5cm2

Question Text	In given figure the area of an equilateral triangle $A BC$ is $17320.5 c m^{2}$ . With each vertex of the triangle as a center, a circle is drawn with a radius equal to half the length of the side of the triangle. Find the area of the shaded region. (Use $π = 3.14$ and $3 = 1.73205$ )
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In given figure the area of an equilateral triangle $A BC$ is $17320.5 c m^{2}$ . With each vertex of the triangle as a center, a circle is drawn with a radius equal to half the length of the side of the triangle. Find the area of the shaded region. (Use $π = 3.14$ and $3 = 1.73205$ )

Text solutionVerified

Practice questions from similar books

In given figure the area of an equilateral triangle ABC is 17320.5cm2. With each vertex of the triangle as a center, a circle is drawn with a radius equal to half the length of the side of the triangle. Find the area of the shaded region. (Use π=3.14 and 3​=1.73205)

Text solutionVerified

Practice questions from similar books

In given figure the area of an equilateral triangle $A BC$ is $17320.5 c m^{2}$ . With each vertex of the triangle as a center, a circle is drawn with a radius equal to half the length of the side of the triangle. Find the area of the shaded region. (Use $π = 3.14$ and $3 = 1.73205$ )