Question

Two cross road each of 5m width runs at right angles through the centre of a rectangular park 70m by 50m such that each is parllel to one of thesides of the park. Find the area of the remaining portion if the park​

Answer 1

Question:-

Two cross road each of 5m width runs at right angles through the centre of a rectangular park 70m by 50m such that each is parallel to one of the sides of the park. Find the area of the remaining portion if the park.

Answer:-

Given:

▪︎Length of rectangular park = 70m

▪︎Breadth of rectangular park = 50m

▪︎Width of both roads = 5m

▪︎Both roads are parallel to length and breadth

▪︎Length of first road parallel to length

= length of rectangle (given it is parallel)

= 70m

▪︎Length of second road parallel to breadth

= breadth of rectangle (given it is parallel)

= 50m

To Find:

▪︎Area of park without road

Steps:

1. Find the area of whole park.
2. Area of both roads.
3. Subtract area of road from area of park.

Solution:

➸Area of rectangular park

= length × breadth

= 70 × 50

= 3500 m²

➸Area of first road parallel to length

= length × breadth

= 70 × 5

= 350 m²

➸Area of second road parallel to breadth

= length × breadth

= 50 × 5

= 250m²

➸Area of common part of road crossing both road at centre of the circle of width 5 m = 5 × 5 = 25m²

➸Area of both roads

= (Area of first road + Area of second road) - common area

= (350 + 250) - 25

= 600 - 25

= 575 m²

➸Area of remaining part of park

= Area of park - Area of roads

= 3500 - 575

= 2925 m²

Hence, Area of remaining part of park is 2925 m².

Formula to be remembered:-

▪︎Area of rectangle = length × breadth

▪︎Area of square = Side × Side

▪︎Area of rhombus = ½ × d¹ × d²

▪︎Area of parallelogram = base × height

▪︎Area of triangle = ½ × base × height