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Find the area of the shaded region in the figure, if AB=5 cm, AC=12 cm and O is the centre of the circle.
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Answer
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Hint: In this question, we use the formula of the area of the semi circle and also the area of the right angle triangle. Area of semi circle is πr22 and area of right angle triangle is 12×(Base)×(Height). In this question we also use the Pythagorean Theorem (Hypotenuse)2=(Perpendicular)2+(Base)2.

Complete step-by-step answer:
Given, AB=5 cm, AC=12 cm and O is the centre of the circle.
To find the area of a semi circle we have to find the radius of the circle.
In ABC we apply Pythagoras Theorem because angle subtended by a diameter on any point of circle is 900 and we know BC is a diameter of circle.
(Hypotenuse)2=(Perpendicular)2+(Base)2(BC)2=(AC)2+(AB)2
Use AB=5 cm, AC=12 cm
(BC)2=(12)2+(5)2(BC)2=144+25(BC)2=169
Take square root,
BC=13cm
The Diameter of the circle is 13cm so the radius of the circle is 6.5cm.
Now, Area of semicircle =πr22
π×(6.5)22
Use value of π=3.14
3.14×(6.5)2266.3325cm2
So, the area of the semicircle is 66.3325 cm2.
Now we find area of right angle triangle ABC ,
Area of ABC=12×(Base)×(Height)Area of ABC=12×(AC)×(AB)Area of ABC=12×(12)×(5)Area of ABC=30cm2
Now, the area of shaded region = Area of semi circle- area of right angle triangle ABC .
Area of shaded region = 66.332530Area of shaded region = 36.3325cm2
So, the area of the shaded region is 36.3325 cm2.

Note: Whenever we face such types of problems we use some important points. First we find the area of the semi circle and also find the area of the right angle triangle then subtract the area of the right angle triangle from the area of the semi circle. So, we will get the required answer.