# On a circular table top of radius 30 cm a design is formed leaving an equilateral triangle inscribed in a circle. Find the area of the design. (π = 3.14)

radius of the circle = 30 cm

Area of the circle = π r2 = 3.14 × 302

= 2826 cm2

PQR is an equilateral triangle

QPR = 60O

QOR = 2 × QPR = 120o

In OQR triangle,

let OS is perpendicular to QR

In triangle OQR as OQ = OR

QOS = QPR = 60O

In triangle OSQ S = 90o

sin 60o =  = QS = 15 √3 cm

Now,

QR = 2 QS = 2 (15 √3) = 30√3 cm

Area of equilateral triangle = × QR2

= × (30√3)2

= 1167.75 CM2

Area of design = Area of circle - area of triangle PQR

= 2826 – 1167.75

= 1658.25 CM2

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