In the following figure a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.
Answers
Answer:
The area of shaded region is 252 cm².
Step-by-step explanation:
GIVEN :
OABC is a square , OA = 21 cm
In the figure join OB.
OB is the diagonal of a square.
Diagonal of a square = √2 × side
= √2 × 21
Diagonal of a square = 21√2 cm
Radius of circle,r = Diagonal of a square = 21√2 cm
Radius of circle,r = 21√2 cm
Area of quadrant, OPBQ = ¼ × πr²
= ¼ × 22/7 × (21√2)²
= ¼ × 22/7 × 441 × 2
= 11 × 63
= 693 cm²
Area of quadrant, OPBQ = 693 cm²
Area of square, OABC = Side² = 21² = 441 cm²
Area of shaded region = Area of quadrant ,OPBQ - Area of square,OABC
= 693 - 441
= 252 cm²
Area of shaded region = 252 cm²
Hence,the area of shaded region is 252 cm².
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