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**Question 1. KGB schools provide free education to girls students from weaker sections. The local body of a town want to open a KGB school in the town for which a rectangular plot ABCD, as shown in the following figure, is very suitable. But this plot belongs to Rati Ram. Rati Ram agrees to exchange it with triangular plot PQR as shown in the same figure. The co-ordinates of the vertices of both the plots are shown in the figure:**

**(i) Compare the areas of both the plots.****(ii) Which mathematical concept is used in the above problem?****(iii) By opening KGB school in the town, which value is depicted by the local body?****Solution.** (i) For rectangle ABCD:

AB = 8 â€“ 2 = 6 units Length

AD = 12 â€“ 8 = 4 units Breadth

âˆ´ Area of rectangle ABCD = AB Ã— AD

= 6 units Ã— 4 units

= 24 sq. units.

For triangle PQR:

QR = 12 â€“ 4 = 8 units Base

SP = 6 â€“ 0 = 6 units Height

âˆ´ Area of DPQR

= 24 sq. units.

â‡’ [area of rect. ABCD] = [area of Î”PQR]

(ii) Co-ordinate Geometry.

(iii) Community or social upliftment.

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