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A rectangular field is 50 m by 40 m. It has two roads through its center, running parallel to its sides. The width of the longer and shorter roads are 1.8 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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1214.5 m 2

1414.5 m 2

1614.5 m 2

1814.5 m 2

answer is D.

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Detailed Solution

Given a rectangular field is 50 m by 40 m.
R.D. Sharma Solutions Class 7 | Math Chapter 20 Mensuration I (Perimeter and Area of Rectilinear Figures) Exercise 20.2

R.D. Sharma Solutions Class 7 | Math Chapter 20 Mensuration I (Perimeter and Area of Rectilinear Figures) Exercise 20.2

Area of rectangle is

l e n g t h × b r e a d t h

Area of the rectangular field ABCD is,

⇒ A = 50 m × 40 m

⇒ A = 2000 m 2

Area of the road KLMN is,

⇒ A = 40 m × 2.5 m

⇒ A = 100 m 2

Area of the road PQRS is,

⇒ A = 50 m × 1.8 m

⇒ A = 90 m 2

Area of EFGH is,

⇒ A = 2.5 m × 1.8 m

⇒ A = 4.5 m 2

Area of the roads = Area of KLMN + area of PQRS – Area of EFGH

⇒ A = 100 m 2 + 90 m 2 − 4.5 m 2

⇒ A = 185.5 m 2

Area of the remaining portion of the field = Area of the rectangular field ABCD – Area of the roads

⇒ A = (2000 − 185.5) m 2

⇒ A = 1814.5 m 2

Therefore, the area is

1814.5 m 2

.
Hence, option 4 is correct.

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