Chapter 11: Areas and Its Boundary

4 times

24 cm

2 times

Save the Birds:

There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motor boats in only one lake. The other lake will be saved for the birds to make their nests.

a) How many cm is the length of the boundary of Lake A in the drawing? _____________ (use thread to find out)

When we measure the boundary of Lake A with the help of thread, it comes out to be around 30 cm.

b) What is the length of the boundary of Lake B in the drawing?

When we measure the boundary of Lake B with the help of thread, it comes out to be around 25 cm.

c) How many kilometers long is the actual boundary of Lake A?

Here, the scale is 1 cm = 1 km

So, length of the actual boundary of lake A = 30 km

d) How many kilometers long is the actual boundary of Lake B?

Here, the scale is 1 cm = 1 km

So, length of the actual boundary of lake B = 25 km

e) A longer boundary around the lake will help more birds to lay their eggs. So which lake should be kept for birds? Which lake should be used for boats?

The boundary around the lake A is more than the boundary around the lake B. So, Lake A should be kept for birds and Lake B should be used for boats.

f) Find the area of Lake B on the drawing in square cm. What is its actual area in square km?

Lake B has 15 fully filled squares and 11 half-filled or more than half – filled squares. Area of 15 fully filled squares = 15 × 15 = 225 square cm

We consider the area of every single half – filled or more than half – filled square as 1 square cm

Thus, the area of 11 such squares = 11 × 11 = 121 square cm

So, total area of lake B = 225 + 121 = 346 square cm

We are given 1 cm on drawing = 1 km on ground

Therefore, 346 square cm on drawing = 346 km

King’s Story:

The King was very happy with carpenters Cheggu and Anar. They had made a very big and beautiful bed for him. So as gifts the king wanted to give some land to Cheggu, and some gold to Anar. King’s Story Cheggu was happy. He took 100 metres of wire and tried to make different rectangles. He made a 10 m × 40 m rectangle. Its area was 400 square metres. So he next made a 30 m × 20 m rectangle.

Area of rectangle = 30 × 20 = 600 square m.

Yes, it is more than the first rectangle.

Following rectangles are possible:

5 × 45 = 225 square m

15 × 35 = 525 square m

25 × 25 = 625 square m

The square will have the biggest area.

Because none of the rectangles will have area 0f 800 square meter.

As the area of rectangle A is shown as 40 m × 20 m.

So, the length of rectangle = 40 m Width of rectangle = 20 m

Gold wire for A = 40 + 20 + 40 + 20 = 120 metres

ii. Gold wire for B = _________ metres

As the area of rectangle B is shown as 80 m ×10 m.

So, the length of rectangle = 80 m Width of rectangle = 10 m

Gold wire for B =   80 + 10 + 80 + 10 = 180 metres

iii. Gold wire for C = ____________ metres

As the area of rectangle C is shown as 800 m × 1 m.

So, the length of rectangle = 800 m width of rectangle = 1 m

Gold wire for C = 800 + 1 + 800 + 1 = 1602 metres

iv. So he will get ____________ metres of gold wire!!

As the area of rectangle D is shown as 8000 m × 0.1 m.

So, the length of rectangle = 8000 m

Width of rectangle = 0.1 m

Gold wire for C = 8000 + 0.1 + 8000 + 0.1 = 16000 + 0.2 = 16000.2 metres.

So, he will get 16000.2 metres of gold wire.