Question

In the figure given alongside, a rectangular field is of size 25 m x 16.4 m. Two paths parallel to the sides of the rectangle through the centre of the field. The widths of the longer and shorter paths are 1.7 in and 2 m respectively. Find the area of the path. Also, find the area of the remaining portion of the field.

Answer 1

Length of rectangular field, $l=25$m

Width of rectangular field, $b=16.4$m

Length of the shorter path, $l_1=16.4$m

Width of the shorter path, $b_1=2$m

Length of the longer path, $l_2=25$m

Width of the longer path, $b_2=1.7$m

Area of shorter path, $A_1=l_1\times b_1$

$=(16.4\times 2)m^2$

$=32.8m^2$

Area of longer path, $A_2=l_2\times b_2$

$=(26\times 1.7)m^2$

$=42.5m^2$

Thus, Area of the path, $P=A_1+A_2-$Area of common path

$=(32.8+42.5)m^2-(2\times 1.7)m^2$

$=75.3m^2-3.4m^2$

$=71.9m^2$

Area of the rectangular field, $A=l\times b$

$=(25\times 16.4)m^2$

$=410m^2$

Hence area of the remaining position of the field.

$=A-P$

$=(410-71.9)m^2$

$=338.1m^2$.