Question

Find the area of cross section indicated by shaded region of following prisms (a) cm 20cm 16 cm 16 cm​

Answer 1

Answer:

Given AC=24cm,BC=17cm

⇒ ∠ACB=90

o

[ Angle inscribe in semicircle ]

∴ △ACB is right angled triangle.

⇒ (AB)

2

=(AC)

2

+(BC)

2

[ By Pythagoras theorem ]

⇒ (AB)

2

=(24)

2

+(10)

2

⇒ (AB)

2

=576+100

⇒ (AB)

2

=676

∴ AB=26cm

∴ Radius of circle (r)=

2

AB

=

2

26

=13,cm

⇒ Area of circle =πr

2

=3.14×(13)

2

∴ Area of circle =3.14×169=530.66cm

2

⇒ Area of semicircle =

2

530.66

=265.33cm

2

⇒ Area of △ABC=

2

1

×AC×BC

⇒ Area of △ABC=

2

1

×24×10

∴ Area of △ABC=120cm

2

⇒ Area of shaded region = Area of circle - ( Area of semicircle +Area of △ABC )

⇒ Area of shaded region =530.66−(265.33+120)

∴ Area of shaded region =530.66−385.33=145.33cm

2