Question

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.​

Answer 1

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 m2 Area of the road KLMN = 40 m x 2.5 m = 100 m2 Area of the road PQRS = 50 m x 1.8 m = 90 m2 Clearly area of EFGH is common to the two roads. Thus, Area of EFGH = 2.5 m x 1.8 m = 4.5 m2 Hence, Area of the roads = Area of KLMN + Area of PQRS – Area of EFGH = (100 m2 + 90 m2) – 4.5 m2 = 185.5 m2 Area of the remaining portion of the field = Area of the rectangular field ABCD – Area of the roads = (2000 – 185.5) m2 = 1814.5 m2