Answer :

∠ACB = 90°

As angle in a semicircle is a right angle.

So △ABC is a right angled triangle

By Phythagoras theorem, which states, In a right angled triangle

(hypotenuse)^{2} = (base)^{2} + (perpendicular)^{2}

In △ABC

AB^{2} = BC^{2} + CA^{2}

13^{2} = BC^{2} + 12^{2}

169 = BC^{2} + 144

BC^{2} = 25

BC = 5 cm

And we know,

= 30 cm^{2}

= 66.3325 cm^{2}

Area of shaded region = area of semicircle - Area of △ABC

= 66.3325 - 30

= 36.3325 cm^{2}

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