1. In the given figure ABCD is a quadrilateral in which AC = 24 cm, BL ⟂ AC and DM ⟂ AC. If BL = 8 cm and DM = 7 cm, find the area of quadrilateral ABCD.
2. In a quadrilateral-shaped field ABCD, diagonal BD = 36 m. AL ⟂ BD and CM ⟂ BD such that AL = 19 m and CM = 11 m. Find the area of the field.
3. Find the area of pentagon ABCDE in which BL ⟂ AC, DM ⟂ AC and EN ⟂ AC. If AC = 18 cm, AM = 14 cm, AN = 6 cm, BL = 4 cm, DM = 12 cm, and EN = 9 cm.
4. Find the area of hexagon ABCDEF in which BL ⟂ AD, CM ⟂ AD, EN ⟂ AD, and FP ⟂ AD. Given AP = 6 cm, PL = 2 cm, LN = 8 cm, NM = 2 cm, MD = 3 cm, FP = 8 cm, EN = 12 cm, BL = 8 cm, and CM = 6 cm.
5. Find the area of pentagon ABCDE in which BL ⟂ AC, CM ⟂ AD, and EN ⟂ AD. Given AC = 10 cm, AD = 12 cm, BL = 3 cm, CM = 7 cm, and EN = 5 cm.
6. A figure ABCDEF consists of a rectangle surmounted by a trapezium. Rectangle ABCD has base AB = 20 cm and height 20 cm. The trapezium DEFG has bases 6 cm and 20 cm, and height 8 cm. Find the total area enclosed by the figure.
7. In quadrilateral ABCD, diagonal AC = 30 cm, BL ⟂ AC, and DM ⟂ AC. If BL = 9 cm, DM = 7 cm, AL = 12 cm, and MC = 10 cm, find the area of ABCD.
8. Find the area of pentagon ABCDE where AC = 30 m. BL ⟂ AC, DM ⟂ AC, and EN ⟂ AC such that BL = 5 m, DM = 12 m, EN = 8 m. Points divide AC as AM = 10 m, MN = 8 m, NC = 12 m.
9. The field ABCD is kite-shaped with diagonal AC = 28 m. BL ⟂ AC = 7 m and DM ⟂ AC = 9 m. If AL = 10 m and MC = 8 m, find the area of ABCD.
10. Quadrilateral ABCD has AD as base. From B and C, perpendiculars BL and CM are drawn to AD. Given AL = 7 cm, LM = 10 cm, MD = 5 cm, BL = 6 cm, and CM = 4 cm. Find the area of ABCD.
11. Pentagon ABCDE consists of two triangles joined along one side. Triangle ABC has base AC = 18 cm and height 12 cm. Triangle CDE has base CD = 14 cm and height 6 cm. Find the total area of pentagon ABCDE.
12. In quadrilateral ABCD, AB ∥ CD. From B and C, perpendiculars are drawn to AD. Given AB = 10 cm, CD = 18 cm, BL = 7 cm, CM = 5 cm, and LM = 12 cm. Find the area of ABCD.
13. Hexagon ABCDEF is formed by three adjacent trapezia on the same base. Heights are 6 cm, 8 cm, and 5 cm, and upper bases are 6 cm, 10 cm, and 4 cm. The total lower base is 30 cm. Find the total area of ABCDEF.
14. Quadrilateral ABCD has AC = 40 m, BL ⟂ AC = 10 m, CM ⟂ AC = 9 m. If AL = 12 m and MC = 19 m, find the area of ABCD.
15. A structure consists of a rectangle ABCD with base 24 m and height 12 m, and a trapezium CDEF on top of it with bases 24 m and 10 m, and height 6 m. Find the total area of the figure.