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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