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Mensuration 1 | Mensuration 1 Exercise 20.2

Question 11

A rectangular field is 50 m by 40 m. It has two roads through its center, running parallel to its sides. The widths 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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Let ABCD be the rectangular field and KLMN and PQRS the two rectangular roads with width 1.8 m and 2.5 m, respectively.

Given that length of rectangular field = 50 m

Breadth of rectangular field = 40m

Area of rectangular field ABCD = 50 m x 40 m

= 2000 m^2

Area of the road KLMN = 40 m x 2.5 m

= 100 m^2

Area of the road PQRS = 50 m x 1.8 m

= 90 m^2

Clearly area of EFGH is common to the two roads.

Thus, Area of EFGH = 2.5 m x 1.8 m = 4.5 m^2

Hence, Area of the roads = Area of KLMN + Area of PQRS – Area of EFGH

= (100 m^2 + 90 m^2) – 4.5 m^2

= 185.5 m^2

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

= (2000 – 185.5) m^2

= 1814.5 m^2

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Question 11

A rectangular field is 50 m by 40 m. It has two roads through its center, running parallel to its sides. The widths 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.

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

Let ABCD be the rectangular field and KLMN and PQRS the two rectangular roads with width 1.8 m and 2.5 m, respectively.

Given that length of rectangular field = 50 m

Breadth of rectangular field = 40m

Area of rectangular field ABCD = 50 m x 40 m

= 2000 m^2

Area of the road KLMN = 40 m x 2.5 m

= 100 m^2

Area of the road PQRS = 50 m x 1.8 m

= 90 m^2

Clearly area of EFGH is common to the two roads.

Thus, Area of EFGH = 2.5 m x 1.8 m = 4.5 m^2

Hence, Area of the roads = Area of KLMN + Area of PQRS – Area of EFGH

= (100 m^2 + 90 m^2) – 4.5 m^2

= 185.5 m^2

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

= (2000 – 185.5) m^2

= 1814.5 m^2

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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