Question

There is a rectangular field of size 94 m x 32 m. Three roads each of 2 m width pass through the field such that two roads are parallel to the breadth of the field and the third is parallel to the length. Calculate: (i) area of the field covered by the three roads (ii) area of the field not covered by the roads.

Answer 1

Let ABCD be the rectangular field.

From the figure it is clear that two roads which are parallel to the breadth of the field KLMN and EFGH with width 2 m each.

One road which is parallel to the length of the field PQRS with width 2 m.

We have from the question, length of the rectangular field AB = 94 m and breadth of the rectangular field BC = 32 m

Area of the rectangular field = Length x Breadth

= 94 m x 32 m

= 3008 m²

Area of the road KLMN = 32 m x 2 m

= 64 m²

Area of the road EFGH = 32 m x 2 m

= 64 m²

Area of the road PQRS = 94 m x 2 m

= 188 m²

Clearly area of TUVI and WXYZ is common to these three roads.

Thus, Area of TUV1 = 2 m x 2 m = 4 m²

Area of WXYZ = 2 m x 2 m = 4 m²

(i) Area of the field covered by the three roads = Area of KLMN + Area of EFGH + Area (PQRS) – (Area of TUVI + Area of WXYZ)

= [64+ 64 + 188 – (4 + 4)] m²

= 316 m² – 8 m²

= 308 m²

(ii) Area of the field not covered by the roads = Area of the rectangular field ABCD – Area of the field covered by the three roads

= 3008 m² – 308 m²

= 2700 m²