Question

b) A zoo is planned as shown in Fig. 8. Adjacent to it is a triangular car park having
an area of 60 m2. A circular well of diameter 6 m lies inside the zoo.
(i) The entire zoo without the car park is to be planted with lawn grass. Find the
area of the region to be covered with lawn grass.
(ii) Fencing is needed for the car park. Find the length of the fence required.
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Answer 1

Given:

A zoo with car parking of 60 m²

and a circular well of diameter 6 m inside it.

To find:

1. The area of zoo without the car parking and the well
2. Perimeter of car Parking area

Solution:

1.Parking is a right triangle

Given ar ( Δ ACM) = 60 m²

So $60=\frac12 ( AC \times AM)$

120= AC × 12

$AC = \frac{120}{12} = 10 cm$

Ar( Trap ABCD)

=$\frac{(AB+CD)\times AC}{2}$

$=\frac{(24+12)\times10}{2}$

=180 m²

Thus area of zoo =180 cm

Area of zoo excluding parking=180-60=120 m²

Now area of well=πr²

=3.14 x 3 x3=28.26 m²

Thus area of the region to be covered with lawn grass

=120-28.26

=91.74 m²

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2. Fencing length =perimeter of Δ ACM

= CA+AM+MC

=10+12+23 ( MC= BD=23 m)

=45 m

Thus the length of fencing =45 m