Question

In Fig. 15.75, OE = 20 cm. In sector OSFT, square OEFG is inscribed. Find the area of the shaded region.

Answer 1

228cm

Step-by-step explanation:

⇒ OE=OG=GF=FE=20cm [ Sides of squares ]

⇒ In right angled △OEF,(OF)

2

=(OE)

2

+(EF)

2

⇒ (OF)

2

=(20)

2

+(20)

2

⇒ (OF)

2

=400+400

⇒ (OF)

2

=800

∴ OF=20

2

cm

∴ OF=r=20

2

cm

⇒ Area of sector OSFT=

360

o

θ

πr

2

here θ=90

o

⇒ Area of sector OSFT=

360

o

90

o

×3.14×(20

2

)

2

⇒ Area of sector OSFT=

4

3.14×800

=628cm

2

⇒ Let a=20cm

⇒ Area of square OEFG=a

2

=(20)

2

=400cm

2

⇒ Area of shaded region = Area of sector OSFT - Area of square OEFG

∴ Area of shaded region =628−400=228cm

2