[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
∴Area of shaded region = Area of ΔABC - Area of 3 sectors
= 17320.5 cm2 - 15700 cm2
= 1620.5 cm2
