Question

5. In the given figure, ABCD is a square with side 10
cm. BFD is an arc of a circle with centre C and
BGD is an arc of a circle with centre A. What is the
area of the shaded region in square centimetres ?
10B
10
(a) 100 - 50 TT
(C) 50 T-100
Ifa tri
(b) 100 – 25 T
(d) 251 - 100​

Answer 1

The  area of the shaded region in square centimetres is 50π - 100 cm^2

Construction - Join BD.

Consider the figure while going through the following steps.

Given,

ABCD is a square with side 10  cm

BED is an arc of a circle with centre C

BFD is an arc of a circle with centre A

From figure, it's clear that,

Area of triangle Δ ABD = Area of triangle Δ BCD

Area of quadrant ABFD = Area of quadrant BCDE

Area of shaded portion

= (Area of quadrant ABFD - Area of Δ ABD)

+  (Area of quadrant BCDE - Area of Δ CBD)

Area of shaded portion = (πr^2/4 - 1/2bh) + (πr^2/4 - 1/2bh)

= 2 (πr^2/4 - 1/2bh)

here, r = h =side of given square  = 10 cm

= 2 (π × (10)^2 /4 - 1/2 × 10 × 10)

= 2 (25π - 50)

∴ The area of shaded portion = 50π - 100 cm^2

Answer 2

Answer:

Option(C)

Step-by-step explanation:

Length of Arc BGD= Length of arc BFD

Since AB=BC=10

Construction: Join BD

As the given figure is a square, so area of ΔABD= Area of ΔBCD

and Area of Quadrant ABGD= Area of Quadrant BCDF

Now, area of shaded region =2(Area of Quadrant ABGD− Area of ΔABD)

A=2(

4

πr

2

−

2

1

×b×h)

Here, r=10,b=h=10

Therefore, A=2(25π−50)

So, area of shaded region =50π−100.