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From a circular piece of paper of area 3850 cm2, an equilateral triangle of area 16√3 cm2 and a regular hexagon of area 486√3 cm2 is cut, then what percent of perimeter is cut from the circle?

From a circular piece of paper of area 3850 cm2, an equilateral triangle of area 16√3 cm2 and a regular hexagon of area 486√3 cm2 is cut, then what percent of perimeter is cut from the circle? Correct Answer 60%

Given:

Area of circle = 3850 cm2

Area of equilateral triangle = 16√3 cm2

Area of regular hexagon = 486√3 cm2

Formula used:

Area of circle = π × (radius)2

Area of equilateral triangle = √3/4 × (side)2

Area of regular hexagon = 3√3/2 × (side)2

Circumference of circle = 2 × π × radius

Perimeter of equilateral triangle = 3 × side

Perimeter of regular hexagon = 6 × side

Calculation:

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Let radius of circle, side of triangle and side of hexagon is ‘r’, ‘a’ and ‘b’ respectively.

Now,

πr2 = 3850

r = 35 cm

Perimeter of circle = 2πr

= 220 cm

√3a2/4 = 16√3

a2 = 64

a = 8

Perimeter of triangle = 3a = 24 cm

3√3b2/2 = 486√3

3b2/2 = 486

b2 = 324

b = 18

Perimeter of hexagon = 6a = 108 cm

Perimeter cut from the circle = 24 + 108 = 132 cm

∴ Required percentage = (132/220) × 100 = 60%

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