33. Calculate the area other than the area common between two quadrants of circles of
radius 14 cm each, which is shown as the shaded region in the adjoining figure.
Answers
The area other than the area common between two quadrants of circles of radius 14 cm each, which is shown as the shaded region in the adjoining figure is 84 cm².
Step-by-step explanation:
It is given that,
ABCD is a square with side 14 cm.
Step 1:
Join the points B and D.
Since each angle in a square is 90° ∴ ∠BAD = 90° and ΔABD is a right-angled triangle.
Considering the given figure,
The area of the minor segment BED is given by,
= [Area of the sector ABED] – [Area of the right ∆ABD]
= [πr² × (θ/360)] – [½ × AD × AB]
Here r = AD = AB = 14 cm and θ = 90°
= [(22/7) × (14)² × (90/360)] – [½ × 14 × 14]
= 154 – 98
= 56 cm²
Step 2:
Similarly, we can also solve for the area of the minor segment BFD which will also be equal to 56 cm².
Therefore,
The total area of both the minor segments is given by,
= 2 * area of one of the minor segments
= 2 * 56
= 112 cm²
Step 3:
The area of the square ABCD will be = side² = 14² = 196 cm²
Thus,
The area of the shaded region in the given figure is given by,
= [Area of the square ABCD] – [Total area of the two minor segments]
= 196 – 112
= 84 cm²
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