Question

With vertices A, B and C of a triangle ABC as centres, arcs are drawn with
radius 6 cm each in fig. IfAB= 20 cm, BC= 48 cm and CA=52 cm, then find the
area of the shaded region.
А
52 cm
20 cm
С
B
48 cm​

Answer 1

Given:-

a=BC=48cm

b=AC=52cm

c=AB=20cm

Semi-perimeter of △ABC=

2

a+b+c

=

2

52+48+20

=60cm

By using Heron's formula,

Area of triangle,

=

s(s−a)(s−b)(s−c)

=

60(60−48)(60−52)(60−20)

=480cm

2

Now,

Area of sectors =

360

πθ

r

2

=

360

πr

2

(θ

1

+θ

2

+θ

2

)

=

360

3.14×36

×(180)=56.52cm

2

Therefore,

Area of shaded region = Area of triangle − Area of sectors

⇒ Area of shaded region =480−56.52=423.48cm

2

hope it helps...