Question

Sides of a triangular field are 14 m,14 m and 14 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field(Use pi = 22/7)
(i) Draw a suitable figure
(ii) Find the area of the triangular field
(iii) Find the area of the field which can be grazed by buffalo
(iv) Find the area of the field which can be grazed by the three animals
(v) Find the area of the field which cannot be grazed by the three animals
(vi) If a circular pond is to be built in the centre of the field so that the three animals can drink water from it, what must be the minimum radius.

Answer 1

Given radius of each sector=7m

Now area of sector with ∠C=

360

∠C

×πr

2

=

360

∠c

×π(7

2

)m

2

Area of the sector with ∠B=

360

∠B

×πr

2

=

360

∠B

×π(7

2

)m

2

And area of the sector with ∠H=

360

∠H

×πr

2

=

360

∠H

×π(7

2

)m

2

Therefore sum of the areas =

360

∠C+∠B+∠H

×π×49=77m

2

Semiperimeter=24 m

Therefore area of the triangular field =

s(s−a)(s−b)(s−c)

=24

21

m

2

So area which can not be grazed =(24

21

−77)m

2

______

Okey