# What is the area (in cm2) of a circle circumscribing a triangle whose sides are 28 cm, 45 cm and 53 cm?

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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