Ex 11.4, 6 Two cross roads, each of width 10 m, cut at right angles through the centre of a rectangular park of length 700 m and breadth 300 m and parallel to its sides. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.
Our figure looks like
We need to find area of park without the cross roads
So,
Area of park without cross roads
= Area ABCD − Area EFGH − Area IJKL + Area PQRS
Note: Here we add area PQRS because it gets subtracted twice
Area of ABCD
ABCD is a rectangle with
Length = l = 700 m
Breadth = b = 300 m
Area of ABCD = l × b
= 700 × 300
= 2,10,000 m2
Area of EFGH
EFGH is a rectangle with
Length = l = 10 m
Breadth = b = 300 m
Area of EFGH = l × b
= 10 × 300
= 3,000 m2
Area of IJKL
IJKL is a rectangle with
Length = l = 700 m
Breadth = b = 10 m
Area of IJKL = l × b
= 700 × 10
= 7,000 m2
Area of PQRS
PQRS is a square with
Side = a = 10 m
Area of PQRS = a × a
= 10 × 10
= 100 m2
Now,
Area of park without cross roads
= Area ABCD − Area EFGH − Area IJKL + Area PQRS
= 210000 − 3000 − 7000 + 100
= (210000 + 100) − (3000 + 7000)
= 210,100 − 10,000
= 200100 m2
= 200100 × 1/10,000 hectares
= 200100/10000 hectares
= 2001/100 hectares
= 20.01 hectare
Area covered by roads
Area covered by the roads
= Area of IJKL + Area of EFGH − Area of PQRS
= 70,000 + 3,000 − 100
= 10,000 − 100
= 9900 m2
= 9900 × 1/10000 hectares
= 9900/10000 hectare
1 hectare = 10,000 m2
10,000 m2 = 1 hectare
1 m2 = 1/10,000 hectare
= 99/100 hectare
= 0.99 hectares
∴ Cross roads cover 0.99 hectare and
remaining area of park is 20.01 hectare

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!