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What is the area (in cm2) of a circle circumscribing a triangle whose sides are 28 cm, 45 cm and 53 cm?
1. \(506\frac{1}{4}\pi \)
2. \(508\frac{1}{2}\pi \)
3. \(718\frac{1}{2}\pi \)
4. \(702\frac{1}{4}\pi \)

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Correct Answer - Option 4 : \(702\frac{1}{4}\pi \)

Given:

Sides of triangle = 28 cm, 45 cm, 53 cm

Concept:

The circum-radius of a right angled triangle is equal to half of the hypotenuse.

Formula used:

Area of circle = \(\pi \)r2

Calculation:

∵ (28)2 + (45)2 = (53)2

∴ The triangle formed by sides 28 cm, 45 cm and 53 cm is a right angled triangle.

∴ Circum-radius of the circle = 53/2 cm

∴ Area of the circle = \(\pi \) × (53/2)2 

\(\pi \) × (2809/4)

\(702\frac{1}{4}\pi \) cm2

 

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