4 Mark Question

Question

There is a rectangular field of size 94 m 32 m. Three roads each of 2 m width pass through the field such that two roads are parallel to the breadth of the field and the third is parallel to the length. Calculate: 1. Area of the field covered by the three roads. 2. Area of the field not covered by the roads.

Vidyadip · Accepted Answer

Here, Two roads which are parallel to the breadth of the field KLMN and EFGH with width 2 m each. One road which is parallel to the length of the field PQRS with width 2 m .
Length of the rectangular field $A B=94 m$ and breadth of the rectangular field $B C=32 m$
Area of the rectangular field $=$ Length $\times$ Breadth $=94 m \times 32 m=3008 m^2$
Area of the road KLMN $=32 m \times 2 m=64 m^2$
Area of the road $EFGH =32 m \times 2 m=64 m^2$
Area of the road PQRS $=94 m \times 2 m=188 m^2$
Clearly area of TUIV and WXYZ is common to these three roads.
Thus, Area of TUIV $=2 m \times 2 m=4 m^2$
Area of $W X Y Z=2 m \times 2 m=4 m^2$
Hence,

Area of the field covered by the three roads: $=$ Area(KLMN) + Area(EFGH) + Area(PQRS) $-\{$ Area(TUIV) + Area(WXYZ) $\}$

$=[64+64+188-(4+4)] m^2$
$=316 m^2-8 m^2$
$=308 m^2$

Area of the field not covered by the roads: = Area of the rectangular field $A B C D$ - Area of the field covered by the three roads

$=3008 m^2-308 m^2$
$=2700 m^2$

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