Question

The parallel sides of a field in the shape of a trapezium are 20 m and 41 m and the remaining two sides are 10 m and 17 m. Find the cost of levelling the field at the rate of Rs 30 per square metre ? 

(a) Rs 6400 

(b) Rs 7320 

(c) Rs 7500 

(d) Rs 7000

Answer 1

(b) Rs 7320

DC = 41 m (Given) 

∴ DE + FC = 41 – 20 = 21m 

Let DE = x, therefore 

FC = (21 – x)

From ΔADE AE² , = (10)² – x² = 100 – x² 

From ΔBCF BF² , = (17)² – (21 – x)² 

= 289 – (441 + x² – 42x) 

= – x² + 42x – 152 

Since AE = BF, 100 – x² = –x² + 42x – 152 

⇒ 42x = 252 ⇒ x = 6 

∴ AE = BF = \(\sqrt{100-6^2}\) = 8

∴ Area of the trapezium ABCD 

= Area of Δ AED + Area of Δ BCF + Area of rectangle ABEF 

= \(\bigg(\frac12\times8\times6\,+\frac12\times15\times8\,+20\times8\bigg)\)m2 

= (24 + 60 + 160) m² = 244 m² 

∴ Cost of levelling the field at Rs 30 per m² 

= Rs (244 × 30) = Rs 7320.