Question

13. A rectangular field is 50 m by 40 m. It has two roads through its centre, running parallel to
its sides. The width of the longer and the shorter roads are 2 m and 2.5-m-respectively.
Find the area of the roads and the area of the remaining portion of the field.
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Answer 1

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Step-by-step explanation:

Area of the longer road=2×50=100m²

Area of the smaller Road =

2.5×40= 100 m²

area of fields=50×40=2000m²

area common to both the road

=2.5×2=5m²

area of roads=200-5=195

=1805m²=ANSWER

Answer 2

Let ABCD be the rectangular field and KLMN and PQRS be the two rectangular roads with width 2.5 m and 2 m, respectively.

Length of the rectangular field CD = 50 cm

Breadth of the rectangular field BC = 40 m

∴ Area of the rectangular field ABCD = 50 m 40 m = 2000 m2

Area of road KLMN = 40 m 2.5 m = 100 m2

Area of road PQRS = 50 m 2 m = 100 m2

Clearly, area of EFGH is common to both the two roads.

∴ Area of EFGH = 2.5 m 2 m = 5 m2

∴ Area of the roads = Area (KLMN) + Area (PQRS) − Area (EFGH)

= (100 m2 + 100 m2) − 5 m2 = 195 m2

Area of the remaining portion of the field = Area of the rectangular field (ABCD) − Area of the roads

= (2000 − 195) m2

= 1805 m2

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