New Millennium Academy

1. Bir Bahadur has a trapezium-shaped land with parallel sides \(20\text{ m}\) and \(24\text{ m}\) and a height of \(10\text{ m}\). There is a rectangular basketball court of length \(10\text{ m}\) and breadth \(8\text{ m}\). The rest of the land is covered with green grasses.

2. Karki bought a land which is a rhombus in shape of area \(360\text{ m}^2\). The measurement of one diagonal is \(36\text{ m}\). He has constructed an equilateral triangle-shaped pool in the land of side \(6\text{ m}\) and depth \(2.5\text{ m}\).

3. Rox bought a land in the shape of a parallelogram with a base of \(24\text{ m}\) and its measured height is \(18\text{ m}\). He constructed a cafeteria in the shape of a kite with diagonals \(8\text{ m}\) and \(12\text{ m}\). The rest of the area is a garden with different flowers and an outdoor sitting space.

4. Ram has Rs 1,00,00,000. He wants to buy a land. He has found a land in the shape of a quadrilateral ABCD with diagonal \(BD = 32\text{ m}\). The height from vertex \(A\) to diagonal \(BD\) is \(AE = 16\text{ m}\), and the height from vertex \(C\) to \(BD\) is \(CF = 18\text{ m}\). The distance \(ED\) is \(x\text{ m}\).

5. Joginder has two plots of land, 'A' and 'B'. Plot-A is trapezium-shaped with top parallel side \(AD = 12\text{ m}\), bottom parallel side \(BC = 18\text{ m}\), and perpendicular height \(8\text{ m}\). Plot-B is rectangular with length \(PQ = 18\text{ m}\) and breadth \(PS = 8\text{ m}\). A road runs horizontally between the two plots.

6. A farmer has a parallelogram-shaped field with a base of \(40\text{ m}\) and a height of \(25\text{ m}\). Inside it, he has dug a triangular pond with a base of \(10\text{ m}\) and a corresponding height of \(12\text{ m}\). The remaining area of the land is used for farming.

7. A kite-shaped signboard has diagonals measuring \(60\text{ cm}\) and \(80\text{ cm}\). It is mounted on the center of a rectangular display board of length \(120\text{ cm}\) and breadth \(90\text{ cm}\).

8. A room's floor is in the shape of a rhombus with diagonals \(12\text{ m}\) and \(16\text{ m}\). The length of each side of the rhombus floor is \(10\text{ m}\). A square carpet of side \(4\text{ m}\) is placed exactly in the middle of the room.

9. An industrial plot is in the shape of a trapezium with parallel sides of \(50\text{ m}\) and \(30\text{ m}\), and a perpendicular distance between them of \(20\text{ m}\). A small equilateral triangle-shaped garden of side \(10\text{ m}\) is maintained at one corner of the plot. (Use \(\sqrt{3} = 1.73\))

10. A school playground is in the shape of a general quadrilateral \(ABCD\) with diagonal \(BD = 40\text{ m}\). The offsets (perpendiculars) from \(A\) and \(C\) to diagonal \(BD\) are \(12\text{ m}\) and \(18\text{ m}\) respectively. An adjacent resting area is in the shape of an isosceles triangle with equal sides of \(13\text{ m}\) and a base of \(10\text{ m}\).