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Home » 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)
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)
Areas Related To Circles | CBSE | Class 10 | Maths | NCERT
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)

Solution:

An equilateral triangle is ABC.

As a result, ∠ A = ∠ B = ∠ C = 60°

There are three sectors, each of which makes a 60°.

The area of ΔABC = 17320.5 cm2

⇒ √3/4 ×(side)2 = 17320.5

⇒ (side)2 =17320.5×4/1.73205

⇒ (side)2 = 4×104

⇒ side = 200 cm

The radius of the circles = 200/2 cm = 100 cm

The area of the sector

= (60°/360°)×π r2 cm2

= 1/6×3.14×(100)2 cm2

= 15700/3cm2

The area of 3 sectors = 3×15700/3 = 15700 cm2

As a result, area of equilateral triangle ABC – Area of 3 sectors = area of the shaded region

= 17320.5-15700 cm2 = 1620.5 cm2

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