Question

26. The Class XII students of a senior secondary school
in Kishangarh have been allotted a rectangular plot of
land for this gardening activity
Sapling of Neem tree are planted on the boundary at a
distance of 1 m from each other. There is a triangular
grassy lawn in the plot as shown in above figure.
The students are to sow seeds of flowering plants on
the remaining area of the plot.
Then, taking A a origin, find the area of the triangle
in this case​

Answer 1

Find the attachment for the answer.

Answer 2

Area of the given triangle is 4.5 square meter.

Step-by-step explanation:

If point A represents the origin of a rectangular plot of land then the coordinates of the points P, Q, and R will be (4, 6),(3, 2),(6, 5) respectively.

Now we know the area of a triangle having three vertices with coordinates$(x_{1}, y_{1}),(x_{2}, y_{2}),(x_{3},y_{3})$ is represented by

Area = $\frac{1}{2}[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]$

Now area of the given triangle = $\frac{1}{2}[4(2-5)+3(5-6)+6(6-2)]$

                                                    = $\frac{1}{2}(-12-3+24)$

                                                    = 4.5 meter square

Therefore, area of the triangle is 4.5 meter²

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