Question

A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 5 to plough 1 m² of the field, find the total cost of ploughing the field.

Answer 1

In the given figure, ABCD is a trapezium having parallel sides 90 m and 30 m.



Draw DE perpendicular to AB, such that DE = BC.

In right angled ∆ADE,
AD² = AE² + ED² (Pythagoras Theorem)
⇒ 100² = (90 − 30)² + ED²
⇒ 10000 = 3600 + ED²
⇒ ED² = 10000 − 3600
⇒ ED² = 6400
⇒ ED = 80 m

Thus, the height of the trapezium = 80 m ...(1)

Now,
Area of trapezium = $\frac{1}{2}\times \mathrm{sum}\mathrm{of}\mathrm{parallel}\mathrm{sides}\times \mathrm{height}$
= $\frac{1}{2}\times \left(90+30\right)\times 80$
= 4800 m²

The cost to plough per m² = Rs 5
The cost to plough 4800 m² = Rs 5 × 4800
= Rs 24000

Hence, the total cost of ploughing the field is Rs 24000.