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

Answer 1

Given: In the trapezium ABCD, the two parallel sides are AB = 90 m, CD = 30 m and EC ⊥ AB.

So, EB = AB – EA = 90 m – 30 m = 60 m

Now, in triangle BEC,

(BC)² = (BE)² + (EC)²

100² = 60² + (EC)²

(EC)² = 10000 – 3600

(EC)² = 6400

EC = `sqrt(6400)`

EC = 80 m

Now, area of trapezium ABCD = `1/2` × (Sum of parallel sides) × (Distance between parallel sides)

= `1/2 xx (AB + CD) xx EC`

= `1/2 xx (90 + 30) xx 80`

= `1/2 xx 120 xx 80`

= 4800 m²

The cost of ploughing the field of 1 m² is Rs. 4.

Now, The cost of ploughing the field of 4800 m² area = 4800 × Rs. 4  = Rs. 19200.

Therefore, the total cost of plughing the field is Rs. 19200.