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?
Answer & explanation
Correct answer: option 3
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