Question : A field is in the shape of a trapezium whose parallel sides are 200 m and 400 m long, whereas each of the other two sides is 260 m long. What is the area (in m2) of the field?
Option 1: 72000
Option 2: 52000
Option 3: 48000
Option 4: 60000
Correct Answer: 72000
Solution :
ABDC is a trapezium AB = 200 m, CD = 400 m, AC = BD = 260 m AB = EF = 200 m and CE = FD ⇒ CD = CE + EF + FD ⇒ 400 = CE + 200 + DF In isosceles trapezium CE = FD ⇒ 2CE = 400 – 200 = 200 ⇒ CE = 100 m In triangle BFD, BC 2 = BF 2 + FD 2 ⇒ (260) 2 = BF 2 + (100) 2 ⇒ BF 2 = 67600 – 10000 = 57600 ⇒ BF 2 = 57600 ⇒ BF = 240 m Area of trapezium = $\frac{1}{2}$ × (Sum of parallel side) × (Distance between parallel side) Area of trapezium = $\frac{1}{2}$ × (400 + 200) × 240 = 120 × 600 = 72000 m 2 Hence, the correct answer is 72000.
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