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What is the area of the shaded region?

O (2577-48) cm²
O (2577-30) cm²
O (25T-24) cm²
O (2577-12) cm²

What is the area of the shaded region? O (2577-48) cm² O (2577-30) cm² O (25T-24) cm-example-1
User Peonicles
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1 Answer

5 votes

Answer:

= (25π - 24) cm²

Explanation:

Area of the circle = πr²

= π(5)²

= 25π cm²

Area of ΔOAB = 2(Area of ΔOCB)

AB = 6 cm

OC = 5 - 1 = 4 cm

By applying Pythagoras theorem in ΔOCB,

OB² = OC² + BC²

5² = 4² + BC²

BC² = 25 - 16

BC = √9 = 3 cm

Area of ΔOCB = 1/2 (OC) (BC)

= 1/2 (4) (3)

= 6cm^2

Area of ΔAOB = 2(6) = 12 cm²

Area of ΔAOB = Area of ΔDOE = 12 cm²

Area of shaded region = 25π - (12 + 12)

= (25π - 24) cm²

User Morepork
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