Question

3. A rectangular field has 80 m length and 48 m breadth. Three roads, each of width 2 m
pass through the field such that two roads are parallel to the breadth and the third road
parallel to the length. Find the area covered by the three roads.
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Answer 1

We know that width of each road is 2m.

Length of two of the roads (parallel to the breadth) = breadth = 48m.

Length of one road (parallel to the length) = length = 80m.

i] Area of two roads parallel to the breadth = 2(width * breadth)

= 2( 2*48)

= 2(96)

= 192 m. square

ii] Area of road parallel to the length = width of road * length

= 2 * 80

= 160 m. square

Now, subtract the areas common in both the roads :

We can see that the length and breadth of these common areas is 2 m.

Areas of the common part = (2*2) + (2*2)

= 4 + 4

= 8 m. square

Upon subtracting these from the total area of the roads :

(192 + 160) - 8

344 m. square

The area covered by the three roads is 344 m. square.

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