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Q.


The Class X students of a secondary school in Krishnagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot. What is the area in which they do not sow seeds?
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a

4.5 sq. units

b

3.5 sq. units

c

5.5 sq. units

d

2.5 sq. units 

answer is A.

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Detailed Solution

Given that, students are participating in a gardening activity in a rectangular plot of land.
Also, sapling of Gulmohar are planted on the boundary at a distance of 1m from each other.
There is a triangular grassy lawn in the plot as shown in the figure.
Question ImageLet the rectangular plot be ABCD and the triangular grassy lawn be PQR.
The students are to sow seeds of flowering plants on the remaining area of the plot.
We know that, the area of triangle formed by any three points whose coordinates are ( x 1 , y 1 ),( x 2 , y 2 ) and ( x 3 , y 3 )   is,
1 2 x 1 (y 2 − y 3 )+ x 2 (y 3 − y 1 )+ x 3   (y 1 − y 2 )  .
To find the area of ΔPQR  , first let us determine the coordinates of the vertices of the triangle PQR.
P 4,6 , Q 3,2 ,R 6,5    ⇒( x 1 , y 1 )=(4,6),( x 2 , y 2 )=(3,2) and ( x 3 , y 3 )=(6,5)  
Putting these values, we have
⇒ 1 2  [4(2−5)+3(5−6) + 6(6−2)]  ⇒ 1 2 [4(−3)+3(−1) + 6(4)] ⇒ 1 2 [−12−3+24] ⇒ 9 2   Area of triangle PQR is 4.5 sq. units.
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