A field is in the shape of a trapezium whose parallel sides are 200 m and 400 m long, whereas each of other two sides is 260 m long. What is the area (in m )of the field? |
48000 52000 72000 60000 |
72000 |
We know that, Area of trapezium = \(\frac{1}{2}\) × (Sum of parallel side) × (Distance between parallel side) Given, The parallel sides = 200 m and 400 m The other two sides = 260 m Here, ABCD is a trapezium AB = 200,CD = 400, BC = AD = 260 AB = EF = 200 cm and DE = FC CD = DE + EF + FC 400 = DE + 200 + DE 2DE = 400 – 200 = 200 DE = \(\frac{200}{2}\) = 100 In △BFC BC2 = BF2 + FC2 (260)2 = BF2 + (100)2 BF2 = 67600 – 10000 = 57600 BF = 240 cm Area of trapezium = \(\frac{1}{2}\) × (400 + 200) × 240 = 120 × 600 = 72000 m2 |