question_answer 1)

                Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.

Answer:

                Fence of the trapezium shaped field \[ABCD=120\text{ }m\] \[\Rightarrow \]               \[AB+BC+CD+DA=120\] \[\Rightarrow \]               \[AB+48+17+40=120\] \[\Rightarrow \]               \[AB+105=120\] \[\Rightarrow \]         \[AB=120105\] \[\Rightarrow \]         \[AB=15\text{ }m\] \[\therefore \] Area of the field \[=\frac{(BC+AD)\times AB}{2}\] \[=\frac{(48+40)\times 15}{2}\] \[=660\,{{m}^{2}}\].