Question

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plz help me solve this question
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Answer 1

Firstly find the hypotenuse by pythagoras theorem, as u can see here that hypotenuse is the diameter of semicircle. So find the area semicircle .
Now find the area of quadrant BAC
And subtract the area of triangle ABC from the quadrant
At last now minus the remaining area from the semicircle
U will get the area of the shaded region
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Answer 2

Hey there !!
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Radius of circle = 14 cm

Area of the quadrant ABMC
= 1/4 × πr²
= 1/4 × 22/7 × 196
= 154 cm²

Area of ∆BAC
= 1/2 × AC × AB
= 1/2 × 14 × 14
= 98 cm²

Area of segment of the circle, BMC
= Area of quadrant ABMC – Area of ∆BAC
= 154 – 98
= 56 cm²

Since, AC = AB = 14 cm and angle BAC = 90°

By Pythagoras Theorem,
BC² = AC² + BC²
BC² = 14² + 14²
BC = √(14² + 14²)
BC = 14√2 cm

Therefore, Radius of semicircle BNC = 14√2 / 2 = 7√2 cm

Area of semicircle BNC
= 1/2 × πr²
= 1/2 × 22/7 × (7√2)²
= 1/2 × 22/7 × 98
= 154 cm²

Hence, the area of the region between two arcs BMC and BNC
= The area of shaded region
= The area of semicircle BNC – The area of segment of the circle BMC
= 154 – 56
= 98 cm²

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