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Please help me solve the question in the above attachment.​

Please Help Me Solve The Question In The Above Attachment class=

Sagot :

[tex]\large\huge\green{\sf{Question:-}}[/tex]

  • 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 Fig. 12.28). Find the area of the shaded region. (Use π = 3.14 and √3 = 1.73205)

[tex]\large\huge\green{\sf{Answer:-}}[/tex]

➡We use the formula for the area of the circle and the area of the triangle to solve the problem.

  • Area of equilateral ΔABC = 17320.5 cm2

➡√3/4 (side)2 = 17320.5 cm2

➡(side)2 = (17320.5 × 4)/√3 cm2

= (17320.5 × 4)/1.73205 cm2

side = √10000 × 4 cm²

= 100 × 2 cm

= 200 cm

∵Radius (r) = 1/2 × (length of side of triangle)

= 1/2 × 200 cm

= 100 cm

  • ∵All interior angles of an equilateral traingle are of measure 60° and all 3 sectors are made using these interior angles.

∴ Angles subtended at the center by each sector (θ) = 60°

  • Area of each sector = θ/360° × πr2

  • Area of 3 sectors = 3 × 60°/360° × πr2

  • = 3 × 1/6 × 3.14 × (100 cm)2

  • = 15700 cm2

∴Area of shaded region = Area of ΔABC - Area of 3 sectors

= 17320.5 cm2 - 15700 cm2

= 1620.5 cm2

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