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 4 to plough 1m2 of the field, find the total cost of ploughing the field.

Question

Philoid · Accepted Answer

PQ = 90m

RS = 30m

QR = 100m

PQ = PT + TQ = 90m

⇒ 30 + TQ = 90

⇒ TQ = 60

In ΔTRQ,

QR² = TR² + QT²

⇒ 100² = TR² + 60²

⇒ TR² = 10000-3600

⇒ TR² = 6400

⇒ TR = 80m

Area (PQRS) =

Area(PQRS) =

Area(PQRS) = 60 × 80 = 4800 m²

Cost of ploughing = Area(PQRS) × Cost per m²

∴ Cost of ploughing = 4800 × 4 = Rs. 19200.