Math, asked by manjujoon196, 4 months ago

In the figure given below, ABC is a right angle triangle where AB = 7 cm and BC = 10 cm.
Given that AEB and BCD are isoscales right angle triangle. Area of the shaded region is
[NSTSE 2011]
C
B
72​

Answers

Answered by kulkarninishant346
0

Step-by-step explanation:

ABC is a right angled triangle where ∠A=90

BC=10cm and AB=6cm

Let O be the centre and r be the radius of the in-circle.

AB,BC and CA are the tangents to the circle at P,M and N

∴IP=IM=IN=r(radius of the circle)

In △BAC,

BC

2

=AB

2

+AC

2

(by pythagoras theorem)

⇒10

2

=6

2

+AC

2

⇒AC

2

=100−36=64

∴AC=8cm

Area of △ABC=

2

1

bh=

2

1

×AC×AB=

2

1

×8×6=24sq.cm

Area of △ABC=Area of △IAB+Area of △IBC+ Area of △ICA

⇒24=

2

1

r(AB)+

2

1

r(BC)+

2

1

r(CA)

⇒24=

2

1

r(AB+BC+CA)

⇒24=

2

1

r(6+8+10)

⇒24=12r

∴r=

12

24

=2cm

Area of the circle=πr

2

=

7

22

×2

2

=12.56sq.cm

Area of shaded region=Area of △ABC−Area of the circle.

=24−12.56=11.44sq.cm

Answered by Atulya123
0

Answer:

85 1/7 cm2

Step-by-step explanation:

85 1/7 cm2

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